This paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple antenna systems with finite-rate feedback. Inspired by the results of classical high resolution quantization theory, the problem of a finite-rate quantized communication system is formulated as a general fixed-rate vector quantization problem with side information available at the encoder (or the quantizer) but unavailable at the decoder. The framework of the quantization problem is sufficiently general to include quantization schemes with general non-mean square distortion functions, and constrained source vectors. The result of the asymptotic distortion analysis of the proposed general quantization problem is presented, which extends the vector version of Bennett?s integral. Specifically, tight lower and upper bounds on the average asymptotic distortion are proposed. The proposed general methodology provides a powerful analytical tool to study a wide range of finite-rate feedback systems. To illustrate the utility of the framework, the analysis of a finite-rate feedback MISO beamforming system over i.i.d. Rayleigh flat fading channels is derived. Numerical and simulation results are presented to further confirm the accuracy of the analytical results.