Gaussian Minimum Shift Keying (GMSK) modulation is widely used in cellular and PCS applications. The popular GSM system uses GMSK. One of the important considerations in the use of modulation is the average power spectral density (psd) and especially the spectral density characteristics on the tails. No method, other than simulation, is currently available to determine the psd of GMSK. In this paper we give closed form expressions for computing the power spectrum using vector-matrix techniques. The psd is expressed in a compact Hermitian form suitable for numerical computation. The psd can be calculated to any desired accuracy by using this method. Results are given for various Gaussian base band filter Bandwidth-Time products and modulation pulse truncation lengths. The formulas given in this paper can be extended to arbitrary pulse shapes and arbitrary modulation indices.