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The mixed projection-mesh scheme of the finite element method was used to set a mixed approximation for three finite elements in the form of a hexagonal eight-node prism with the substitution of displacements after the polylinear law and stress and strain approximation with polynomial interpolation functions, defined for the nodes at the vertices, in the prism center, in the face centers, inner points, and a tetrahedron-shaped element in which displacements are sought in the nodes at the vertices, and stresses and strains are in the nodes at the vertices and in the center. The expressions for the coefficients of the decision matrices are obtained. Several test problems with analytical or known numerical solutions in the elastic statement are examined. The results obtained with the mixed method were compared with those obtained from the finite element method. The relative errors in determining examined characteristics were assessed in the elastic statement. The Irwin plastic zone correction was evaluated in the elastoplastic statement. One of the proposed elements would be appropriate for further application from the solution results and the estimation of time taken for solving specific problems and data body processing. [ABSTRACT FROM AUTHOR]