This paper presents analytical expressions for the multiple-input multiple-output (MIMO) channel capacity in frequency-flat Rayleigh fading environments. An exact analytical expression is given for the er-godic capacity for single-input multiple-output (SIMO) channels. The analysis shows that the SIMO channel capacity can be approximated by a Gaussian random variable and that the MIMO channel capacity can be approximated as the sum of multiple SIMO capacities. The SIMO channel results are used to derive ap-proximate closed-form expressions for the MIMO channel ergodic capacity and the complementary cumula-tive distribution function (CCDF) of the MIMO channel capacity (outage capacity). Simulations show that these theoretical results are good approximations for MIMO systems with an arbitrary number of transmit or receive antennas. Moreover, these analytical expressions are relatively simple which makes them very use-ful for practical computations. This paper presents analytical expressions for the multiple-input multiple-output (MIMO) channel capacity in frequency-flat Rayleigh fading environments. An exact analytical expression is given for the er-godic capacity for single-input multiple-output (SIMO) channels. The analysis shows that the the SIMO channel capacity can be approximated by a Gaussian random variable and that the MIMO channel capacity can be approximated as the sum of multiple SIMO capacities. The SIMO channel results are used to derive ap-proximate closed-form expressions for the MIMO channel ergodic capacity and the complementary cumula-tive distribution function (CCDF) of the MIMO channel capacity (outage capacity). Simulations show that these theoretical results are good approximations for MIMO systems with an arbitrary number of transmit or receive antennas. analytical expressions are relatively simple which makes them very use-ful for practical computations.