This paper describes the analysis of multiple input multiple output (MIMO) Beam forming with adaptive modulation using spectral efficiency as a figure of merit in multipath fading environment. Multipath fading environment causes the transmitted signals to be unreliable due to effects of tall buildings, trees, mountains, moving objects and so on. As a result of increase in demand for information communication technology which is an aspect of wireless communication, this motivated this research work. The system model for MIMO beam forming mode is developed for a 2x2, 3x3 and 4x4 antenna systems configuration in the presence of frequency selective Rayleigh fading channel. A closed- form expression for spectral efficiency is also developed. Received signal strength indication (RSSI) is used for channel estimation in order to change the constellation sizes of the M-ary Phase Shift Keying (M-PSK) modulation scheme in accordance with the fading severity. The analysis is carried out using randomly generated data in MATLAB application package. The results obtained show that the Spectral Efficiency increases as the SNR increases, also as the antenna configurations increase, the average spectral efficiency also increases. This indicates that bandwidth is fully optimized at higher antenna configuration. Mobile wireless designers can find the results obtained useful in the design of improved wireless systems.