In this study, we propose a stochastic multiscale method to predict macroscopic material responses associated with uncertainties of microstructure in heterogeneous materials. Within the proposed multiscale method, a stochastic unit cell (SUC) is defined as a finite-sized volume element in which the uncertainties are uniquely determined by random variables. In the framework of the stochastic collocation method, the expected values of the physical quantities such as stresses and strains are computed as the macroscopic response by Gaussian quadrature from the volumetric averages of physical quantities in the SUCs, which are discretized by Lagrange polynomials at the collocation points. Instead of the conventional condition in which either the volumetric average of stresses or strains is constrained as constant across the SUCs, we present two types of novel boundary conditions to account for the interaction between them. Under the novel boundary conditions, the governing equations of the SUCs are simultaneously solved to determine the expected values of stresses under a given expected value of strains. Throughout several numerical examples, the capability of our proposed multiscale method is demonstrated by comparing the numerical results with those of the direct numerical simulation(DNS) of the microstructure as the reference solution. In addition, the numerical results obtained by our proposed method under the new boundary conditions and the conventional constrained condition for the strain are compared with those of the DNS to confirm the effectiveness.