In this chapter, the problems of stochastic finite-time boundedness (SFTB) and input-output stochastic finite-time stabilization (IO-SFTS) are discussed and addressed for a class of Markov jump systems (MJSs) with unknown nonlinearities and external disturbances. Firstly, under transient state constraints, a suitable sliding mode controller is constructed to drive the state trajectories onto the specified sliding surface during a specified finite (possibly short) time interval. By utilizing the proposed partition strategy, the SFTB is, respectively, analyzed over reaching phase and sliding motion phase during the specified finite time interval. Secondly, further considering transient output constraints with parameter uncertainties, the practical issue that the transition rates (TRs) cannot be completely available is addressed by designing a parameter-related sliding mode control (SMC) strategy. The sufficient conditions are derived to ensure the IO-SFTS of the closed-loop systems over the finite-time interval including the reaching phase and the sliding motion phase, which combined with the proposed sliding mode controller forms the IO-SFTS framework of SMC. Finally, two examples are, respectively, given to illustrate the effectiveness of the designed finite-time sliding mode controllers in dealing with state and output constraints.