Approximate second order moments of the squared singular values of the channel matrix of a multiple input multiple output (MIMO) system are derived. Correlation at both the receiver and the transmitter antenna arrays is allowed, The approximation converges to the true moments as either the number of transmit or receive antennas increases. Simulations indicate that the derived moments may provide a good approximation of the true moments even for realistic array sizes. As an application, an expression for the mean channel capacity is derived. The expression is simple enough to provide insight while offering promising performance when compared with simulated channel capacities.