This paper outlines an efficient approach to evaluate the performance of bit interleaved coded modulation (BICM) systems. Most of the approaches suggested so far evaluate the probability of individual pairwise error events and obtain an union bound to the bit error probability. This gives very tight bounds on performance for SNR's above cutoff rate for BPSK modulation. However, for higher order modulation systems, the number of bit errors in a symbol slot depend on the exact two modulated symbols involved in an error event and the linearity of the code cannot be extended to include the modulator. The performance is usually approximated by a few dominant error events which is applicable to AWGN channels. Some approaches consider infinite depth interleaving to obtain a simplified linear model. In this paper, we study the evaluation and convergence of union bounds for fading channels with finite code block sizes. We develop a general approach which assumes an ideal model for the modulator and enables us to extend the linearity of the considered codes to simplify the computation. This enables us to analyze the performance of concatenated codes with an interleaver of finite length. The approach also gives greater insight into the influence of modulator parameters and block length of the code on the diversity achieved in bit interleaved coded modulation systems. The application of our analytical model is demonstrated with examples and simulations.