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The work is devoted to the problem of initial neutron source distribution for modeling kinetic transient processes by the direct analogue Monte Carlo method. An algorithm is proposed for modeling such a source. The source algorithm implemented in the KIR2 program and designed to solve the problem of taking the system out of the critical state by introducing a perturbation (reactivity). Only prompt neutrons are considered. For the neutron source distribution, a phase coordinates of the neutron are used. The phase coordinates are determined in the preliminary calculation of the critical state. The results of testing the algorithm on non-stationary test problems (an infinite environment and RP1GS) are presented. In each task, the geometric area is filled with material presented in the form of single-group macroparameters. The results of calculating the integral neutron flux density were compared with the solution of the point kinetics equations. Good agreement was obtained - the deviation during all the calculated processes does not exceed 0.4 % in the integrated flux density, but it increases at the end of the processes with the introduction of negative reactivity up to 2.5 % with a small number of neutrons in the system.