Lossless audio compression is a rapidly developing field with a strict stipulation: the decompressed sample information must match the original audio data. A common strategy applied by modern compression systems is a "prediction/residual " structure. This strategy generates a series of estimates for audio samples and applies coding schemes to encode the residuals (the differences between the actual values and theestimates). This thesis studies two main areas of the "prediction/residual" structure: residual coding and blocking, and their respective algorithms. A common algorithm for residual coding is Golomb-Rice coding, a simple general-purpose integer coding algorithm. It takes advantage of the fact that the distribution of the residuals output from a prediction model generally follows a Laplacian distribution. Based on the study of Golomb-Rice coding, a new residual coding scheme,Golomb-Rice with Huffman coding (GRHC) is designed. GRHC coding can produce codes that can be adapted (to a degree) to the actual distribution of the residuals output from linear prediction model. Furthermore, a new idea, flexible blocking, is introduced. Instead of blocking the sequence of samples into fixed length blocks, the algorithm can flexibly block samples to produce an improved compression ratio. This thesis introduces two flexible blocking schemes and an extreme block size search scheme, as well as implements two of these methods in an open-source codec - FLAC.