In this paper, we consider single server queueing system with a finite buffer, MAP input and independent generally distributed service times. Customers are selected for the service in accordance with the LIFO (Last In – First Out) service discipline. It is well known that stationary distribution of the number of customers in such a system coincides with the corresponding distribution in the system with FIFO (First In – First Out) discipline which has been studied in the literature early. In the present research we focus on investigating the stationary distribution of waiting (sojourn) time in the system.