The paper presents solutions of the three-dimensional problem of the theory of elasticity, when displacements are prescribed on the boundaries of parallel cylindrical cavities in an elastic space. The solution is obtained by the generalized Fourier method with respect to the system of Lame equations in cylindrical coordinates associated with cylinders. Infinite systems of linear algebraic equations, to which the problem is reduced, are solved by the truncation method. As a result, displacements were found, followed by stresses in the elastic body. Numerical results are given for the case of two cylinders.
cylindrical cavities in space, Lame equations, generalized Fourier method