The formulas obtained in [10, 12] for the calculation of nodal reactions and stiffness matrix coefficients allow to use different systems of coordinate functions constructed on the basis of polynomials to represent displacements. A distinctive feature of these relations in comparison with similar ones derived when using Fourier series to representthe displacements is that the coefficients of not only diagonal, but also peripheral submatrices do not equal zero and the solution of systems of equations obtained on their basis by direct methods becomes impractical. The factors that determine the efficiency of the semi-analytical finite element method include, first of all, the task of fixing the conditions at the ends of the body and the amount of calculations due to the rate of convergence of the integration process of solving systems of equations.Of particular importance in the semi-analyticalvariant of the finite element method is the choice of the appropriate system of coordinate functions to represent the displacements along the length of the prismatic element. In deriving the relations of a universal finite element with the exception of Fourier series, the direct use of functions used in the above works to calculate prismatic bodies based on the semianalytic finite element method seems irrational, because each of them satisfies only individual cases of boundary conditions. from the standpoint of the theory of shells. In addition, among thefunctions considered, only Fourier series provide a strict separation of variables and reduce the original spatial problem to a series of two-dimensional for each contained harmonic.Based on the above research, it is concluded that mixed coordinate function systems based on Michlin polynomials allow the simplest formulation of different conditions of fixation at the ends, while ensuring a high rate of convergence of the iterative process.