Scattering of light by ice crystals of cirrus clouds is an important problem for remote sensing of clouds and the atmosphere. Such a solution is necessary for the interpretation of data obtained by active and passive remote sensing instruments, such as lidars and photometers. Ice crystals in cirrus clouds are large non-spherical particles. To solve the problem of light scattering by large non-spherical particles, it is not possible to apply rigorous numerical methods such as FDTD, DDA, PSDT, due to their high computational complexity for large particles. This problem also cannot be solved within the framework of the classical geometrical optics approximation, since this method does not take into account such phenomena as diffraction and interference, which have a significant effect in the vicinity of the backscattering direction. This report presents the solution for the problem of light scattering by non-spherical particles with sizes from 10 to 1000 µm. The results were obtained within the framework of the physical optics approximation. The obtained database of light scattering matrices allows one to improve the accuracy of interpretation of laser sounding data of atmospheric aerosol and crystal clouds for lidars and remote sensing applications..