The extinction matrix for cirrus clouds has been calculated for the visible and infrared regions using the physical optics approximation. The cirrus clouds are modeled as a statistical ensemble of the hexagonal ice plates, distributed over their size and orientations by the gamma and Gaussian laws, respectively. Then, the extinction matrixes as the functions of the incident wavelength, incident direction, crystal size, and crystal orientation are numerically calculated for the first time. It is shown that the off-diagonal elements of the matrix are negligible. Therefore, the extinction in cirrus clouds is described with good accuracy by the scalar exponential law.