In this article we consider a problem of digital simulation of a received signal for SAR, which uses pulse package with chirp. Chirp demodulation is carried out in a receiver mixer by local oscillator, which has chirp with the same steepness. Surface surveillance is performing in a sector scan mode. Surface model contains thousands of resolution elements. It is necessary to calculate hundreds of thousands of time samples for each point. The direct calculation for so many samples results in unacceptable time expenditure. The method of fast calculation is known. This method is based on multiplication of two matrices of samples. The first matrix includes the chirp law and contains samples for one repetition period. The second matrix includes slow processes and contains one sample for each repetition period. Factorization of computational formula speeds up model operation hundreds times as much. However, known method does not allow the peculiarities of pulse package processing in the SAR under consideration. By sector scan, the target has greater radial velocity caused by SAR moving. In the task of modeling of received signal the fast moving makes factorization of computational formula difficult. The method of fast calculation of the received signal for the model of the described SAR is offered in this work. Admissible conditions of practical application of the offered method of analysis are estimated. Compensation of relative motion of SAR is carried out before factorization of the design formula in order to expand the conditions of practical application. The method provided more than 200 times acceleration of the calculation.