In this article, a computationally-efficient approach is presented for Bit Error Rate (BER) calculations in multi-user Multiple Input Multiple Output (MIMO) frequency selective fading environments, operating in spatial multiplexing transmission mode. To this end, theoretical expressions for the equivalent Signal to Interference plus Noise Ratio (SINR) per active user and transmission mode, as well as mean BER, are derived. The key idea is that all parameters related to BER calculations can be expressed as sums of identically distributed random variables (RVs). Hence, computational burden can be reduced, since summation formulas take into account the parameters of a standalone RV along with the correlation of an arbitrary pair of RVs. As results indicate, the proposed approach can accurately estimate mean BER in multiuser MIMO orientations with increased reception diversity order, for arbitrary number of transmit/receive antennas, a modulation scheme, and a number of resolvable multi-path components.