We report on numerical study of the nonlinear pulse propagation under filamentation of femtosecond near-infrared radiation under normal dispersion regime in YAG crystal. Influence of the Raman and Kerr tandem action on a spatial and temporal dynamics of the laser pulse were discussed. We have shown that Raman nonlinearity provides an asymmetry of temporal pulse profile: the leading edge becomes more bright and propagates at larger distances in comparison with trailing edge.