The work is devoted to numerical simulation of the stationary stress-strain state of lattice cylindrical shells made of unidirectional carbon fiber reinforced plastics and to their optimal design. After averaging stiffness characteristics of lattice structure, the displacement and stress formulations for continuum anisotropic equivalents of lattice shells are given on the basis of classical relations of 3D theory of elasticity. While using a special fast pseudo-spectral algorithm, the solutions to problems of axial compression of anisogrid shells are obtained and compared one to another. The algorithm provides exponential decrease of error of approximation and requires small computational resources. Using this algorithm we have found the optimal geometrical parameters of structure ensuring its bearing capacity under given non-uniform loads.