Methods for extracting and amplifying sequences using ancient DNA (aDNA) can be prone to errors caused by post mortem modifications of the DNA strand. A new statistical method is developed for predicting errors in aDNA sequences caused by such processes. In addition to the canonical DNA substitution model parameters, a discrete Markov chain is used to describe nucleotide substitutions occurring via post mortem degradation of the aDNA sequences. A computer program, BYPASSRDEGR was developed implementing the method and was used in subsequent analyzes of simulated datasets under the new model.