We study light-induced deformation of azobenzene elastomers which can display liquid-crystalline (LC) order. It is shown that photomechanical behavior of azobenzene elastomers is determined by the strength of the LC interactions, which is proportional to the density of rodlike azobenzene chromophores. At weak LC interactions, a uniaxial order and uniaxial deformation of azobenzene elastomers along the polarization vector of the light E is observed. At strong LC interactions, the light is able to induce a phase transition from the uniaxial to the biaxial state, with two axes being related to the vector E and to a preferable alignment of the chromophores in the plane perpendicular to E. The phase transition can be of either the first or the second order. Azobenzene elastomers can demonstrate elongation or contraction along the polarization vector E, depending on the orientation distribution of chromophores around the main chains of network strands. The results of the theory are in a qualitative agreement with experiments and computer simulations, which demonstrate biaxial ordering in azo-containing polymers.