Resonant interactions between an electromagnetic wave packet and charged particles based on numerical calculations are investigated. The strong surfatron acceleration of weakly relativistic electrons by an electromagnetic wave packet in space plasma is studied. In the central area of the wave packet, the electric field amplitude is above a threshold value and this makes it possible to capture particles in the surfing mode. The work is carried out by exact solving of second order nonlinear, nonstationary equations for the wave packet phase on the particle's trajectory at the carrying frequency. Numerical modeling shows that the trapping of weakly relativistic electrons in strong acceleration mode occurs immediately for a wide enough range of favorable initial wave phase values (80% and more). Furthermore it has been demonstrated that the combination of ranges of the particle's initial parameters corresponding to the capturing in surfatron acceleration is large enough. Temporal dynamics of velocity components for accelerated particles and the particularities of their trajectory, taking into account cyclotron rotation at the initial stage and phase plane structure for numerically solved nonlinear equations, are considered. Simulation results allow us to draw conclusions about the possibility of surfatron acceleration of weakly relativistic charged particles in space plasma by an electromagnetic wave packet. © 2017