A microphysical model of photophoretic motion of soot aggregates is presented, which takes into account their fractal structure. Comparison with known experimental data is executed, and good qualitative and quantitative agreements are shown. Characteristics of photophoretic motion of fractal-like soot aggregates in the field of atmospheric radiation are calculated. For the model of fractal-like particles, the photophoretic effects with soot aerosol in the stationary atmosphere are the most pronounced in the upper troposphere - middle stratosphere.