Summary: This paper is concerned with the steady-state probability distributions for a well-known parallel queue with two identical servers, each having its own queue. Upon the arrival time, the new arrival joins the shortest queue, and stays in that queue until being served. Jockeying between queues is not allowed. To make the problem solvable, the states of the resulting Markov chain are truncated into a banded array. Two steady-state distributions will be derived by using probability generating function and matrix-geometric method: the probability of queue length and the customer sojourn time. Under certain conditions, the sojourn time has a phase-type distribution. Numerical results are presented and the convergence of the truncated model is discussed.