The mixed problem of bending of a transtropic thick plate and a short cylinder is solved using the Lur'e-Vorovich homogeneous solutions. The most typical results from numerical experiments for a wide range of physical and geometrical parameters are presented Keywords: cylindrical thick transtropic plate, short cylinder, pure bending, Lur'e-Vorovich homogeneous solutions, numerical experiments Solving mixed problems of elasticity for finite cylindrical bodies is a challenge because of the integrable singularities of the stress components at the corner points [1]. The elastic-equilibrium problem for an isotropic finite-length cylinder was solved in [2, 3] by the method of homogeneous solutions and in [4,5] by the superposition method. As to a transtropic body, only an approximate formulation with weakened boundary conditions on the lateral surface and restrained ends was used [6]. Problems for noncircular hollow cylinders were analyzed in [12,13,15].We will discuss results from stress-strain analysis of a short transtropic cylindrical body based on the use of Lur'e-Vorovich homogeneous solutions [7]. These solutions allow obtaining a solution close to the exact one with the help of modern computers. We will also analyze the influence of the type of material and the relative thickness of the elastic body on the stress-strain state (SSS) and estimate the accuracy and applicability limits of the theory of thin plates. The accuracy of the obtained solution will also be determined.