In this paper stochastic and almost sure stability of a Markov jump linear singular system are analyzed. First, it is given a set of coupled generalized Lyapunov equations to characterize the stochastic stability of the system. Second, it is introduced a top Lyapunov exponent to give a sufficient condition for almost sure stability. Our approach captures the solvability issue arising in this class of systems, leading to Lyapunov equations whose parameters reflex the solvability in an explicit manner. Two examples are presented in order to show the effectiveness of the proposed stability analysis.