The BIA (Binary Interaction Approximation) formulation in the presence of neutralizing immovable background ion is presented for analysis of multiple electron motion. Such a BIA scheme is applied to electrons in plasmas. A test calculation shows that 1) the plasma oscillation and its frequency are successfully detected, 2) the CPU time for the BIA are less than 1.5 sec and 1 hour for two and three dimensional analysis, while 127 sec and 13 hours for the direct integration method (DIM) by using a Runge-Kutta-Fehlberg integrator with an absolute error tolerance of 10⁻¹⁶, and 3) the number of time steps for the DIM, in such a case, are as many as 5.8 × 10⁴ and 3.6 × 10⁶, while those for the BIA are only 256 and 512.