Let δ define the thickness of the membrane and cortical cytoskeleton, d is the muscle fiber diameter, and l is its length. Then, we can write the following relations:
, 
This enables us to consider the fiber a long, cylindrical envelope called a thin-walled rod [
It is typical for transversal sections of this kind of objects to initially be plane distorted on a surface: W(x, z). W(x, z) is usually called a sectional warping. For closed envelope rods, including muscle fibers, axial uniform warping is also typical, so we can rewrite W(x, z) as W(x). We have 
in Saint-Venant’s prob-
lem, where Ф is the Prandtl function (underlining indicates that the underlined value is a vector). We can take a sectorial area as W for a thin section. Then, for the part of membrane between the Z-disk and M-line to be considered, we use the thin-walled theory statements. We will consider the cylindrical rod with thin simply connected section F and with volume load f. For simplicity, we suppose the 
end to be fixed, and we have the surface load
, which is a net load between the Zdisk and M-line (to be determined later) on the other end
. We describe this three-dimensional case using the method of variations [
, 
where 
is the translation vector, 
is the volumetric energy, 
is the Lamé constant, 
is the Poisson ratio, 
is the deformation tensor, and 
is the trace of deformation tensor, the first invariant (double underlining indicates tensors).
To derive equations from the variation principle, we approximate the translation as:
where 
is the linear translation, 
is the rotation vector, 
is the rotation angle per unit length, and 
is the warping function:
, 
,
is the basis vector of the Lagrangian coordinate.
Let us suppose that there is a lack of transversal shifts; then:
Taking into account Equation (3), approximation (2) becomes:
That is:
From the classical theory of elasticity, we know that:
where S is the symmetrization symbol.
Using (4), Equation (6) can be rewritten:
where 
and 
.
Then:
Substituting (8) into (1), we obtain a new volumetrical energy density:
Since 
:
where
, and 
is Young’s modulus.
Taking into account (7), (9) becomes:
Integrating (10) in the section:
where
, 
, 
, 
, 
.
Let us now determine the work of volume loads:
where
, 
, 
, 
is the distributed bimoment per unit length.
Similarly, a work of the volume load on the end:
where
, 
, 
, 
is the bimoment on the end.
Taking into account Equations (12) and (13), the variational equation becomes:
From (14), we obtain differential equations and limits:
,
:
, 
, 
,
:
, 
, 
,
,
:
, 
, 
The set of equations derived in (15) gives us a chance to completely describe muscle fiber membrane behavior as a long cylindrical envelope and to find the potential energy 
in the case described.
Let us assume that there is no external moment influence and that section warping and transversal shift contribution are negligible in comparison with the longitudinal component. This assumption is justified because of the specific muscle cell structure. Then, solving (15), we can find
:
where 
is the volume load, 
is the surface load, F is the section area, 
is the adduced Young’s modulus, and 
is the Poisson ratio.
An external mechanical field acts on the whole organism and launches a number of processes, leading to nervous activation change in skeletal muscles, a liquid shift in the cranial direction, and, as a result, to a volume load change in the heart.
These processes results in the muscle fiber membrane becoming subjected to the following forces: 
by the contractile apparatus as a result of nervous activation, 
, hydrostatic pressure (only for cardiomyocytes), and
, the gravity. Nervous activation by intracellular signal mechanisms launch results in mechanical tension that arises in a muscle fiber because of myosin head and actin filament interaction, which is transmitted into the sarcolemma by the cortical cytoskeleton. Let us suppose that this interaction is uniform distributed over the length of the contractile apparatus. Therefore, it can be represented as a periodical function with the period of Т, which equals the distance between two successive myosin heads.
Then
, where 
is the force generated by the single bridge, approximately 3 - 5 pN, n represents a number of bridges, which can be determined as the ratio of the fiber length (l) to the distance between two successive bridges, approximately 43 nm, per fiber volume. Gravity also acts on a muscle cell depending on the cell orientation. The specific volumetric force in this case may be represented as
, where
is the angle between the gravity vector and the fiber longitudinal axis direction, 
is the free-fall acceleration, and 
is the liquid density. The surface load on the end is a net load of gravity and hydrostatic pressure;
, where d is the fiber diameter.
Then, the external forces become:
,