The performance of the Viterbi decoding algorithm in a binary symmetric channel is usually estimated by a lower or an upper bounds of a bit error probability. Nowadays, there are expressions for the exact bit error probability estimation for several trivial convolutional codes. However, traffic in modern systems is packetized. Thus, packet error probability is also an important performance metric. Besides, the existed methods could not be used for the task of packet error probability estimation. Therefore this paper presents an algorithm for the calculation of the exact packet error probability for the Viterbi decoding. The algorithm is based on a recurrent search of the cases, which lead to an error free-decoding and then cumulative probabilities of these cases are calculated.