The reachable set synthesis problem of singular Markovian jump systems (SMJSs) is investigated in this paper. Both state reachable set and output reachable set are considered for SMJSs without delay and with distributed delay. By utilizing proportional and derivative state feedback control technique, sufficient conditions for delay-free SMJSs are proposed to guarantee the reachable set of closed-loop systems to be mean-square bounded by a prescribed ellipsoid firstly. Then the result is extended to SMJSs with distributed delay. Numerical examples are given to demonstrate the effectiveness of the obtained result.