We present a new technical simulator for the eLISA mission, based on state space modeling techniques and developed in MATLAB. This simulator computes the coordinate and velocity over time of each body involved in the constellation, i.e. the spacecraft and its test masses, taking into account the different disturbances and actuations. This allows studying the contribution of instrumental noises and system imperfections on the residual acceleration applied on the TMs, the latter reflecting the performance of the achieved free-fall along the sensitive axis. A preliminary version of the results is presented.