stochastic mechanical behaviors of random media is relevant to various of engineering fields, one example of random media is, in order to simulate the fault formation of earthquake, stochastic treatment on ground surface is applied which consists of several layers of not fully known properties and structures. in this presentation, we examine a general linearized elastostatic problem in random media. a complete analysis in solution space is provided including existence and uniqueness. the single integral formulation of weak form and stochastic collocation method are applied to solve this problem. moreover, the prior error estimators of stochastic collocation method are derived which imply the rate of convergence is exponential along with the order of polynomial increasing in the space of random variables. as expected, the numerical experiments admit the exponential rate of convergence verified by a posterior error analysis. at last, a adaptive strategy derived by the posterior error analysis is designed.