In this present, the stochastic shape/interface optimal control is computationally considered. The control strategy is to minimize the expectation of a tracking cost functional or energy dissipation constrained by a stochastic interface elliptic equation or stochastic Navier-Stokes equations. Stochastic shape variations are used to establish a decreasing sequence of admissible interfaces. The finite element method is used to discretize the state and adjoint systems and provides mesh moving direction. To reduce the computational complexity for uncertainty quantification, the sparse grid collocation method is applied to match the probability distribution for the relatively large scale optimization problems and stochastic sampling-based descent method is considered for the large-scale sampling  optimization. The unrestricted/fixed volume/ fixed surface area constraints are further applied and considered in practical sense. Finally, the numerical results are provided to demonstrate the efficiency and effectiveness of our algorithms.