Surface relief gratings on azobenzene containing polymer films were prepared under irradiation by actinic light. Finite element modeling of the inscription process was carried out using linear viscoelastic analysis. It was assumed that under illumination the polymer film undergoes considerable plastification, which reduces its original Young's modulus by at least three orders of magnitude. Force densities of about 10(11) N/m(3) were necessary to reproduce the growth of the surface relief grating. It was shown that at large deformations the force of surface tension becomes comparable to the inscription force and therefore plays an essential role in the retardation of the inscription process. In addition to surface profiling the gradual development of an accompanying density grating was predicted for the regime of continuous exposure. Surface grating development under pulselike exposure cannot be explained in the frame of an incompressible fluid model. However, it was easily reproduced using the viscoelastic model with finite compressibility. (C) 2004 American Institute of Physics.