The book presents methods of approximate solution of the basic problem of elasticity for special types of solids. Engineers can apply the approximate methods (Finite Element Method, Boundary Element Method) to solve the problems but the application of these methods may not be correct for solids with the certain singularities or asymmetrical boundary conditions. The book is recommended for researchers and professionals working on elasticity modeling. It explains methods of solving elasticity problems for special solids. Approximate methods (Finite Element Method, Boundary Element Method) have been used to solve these problems. The interpolation and the spline-interpolation solutions of the 3D problem of the theory of elasticity have been constructed in this work. The spline-interpolation solution can be considered as a variant of the finite element method.