Abstract: A homotopy-based method for calculating the stochastic responses of a structure under static loads involving random parameters is proposed. In this method, the static equilibrium equation is reconstructed based on the homotopy analysis method, the stochastic responses are represented by an infinite multivariate homotopy series of the random variables and approaching functions, and all the deterministic coefficients in the multivariate series are determined through solving a series of various order of deformation equations. This homotopy series solution obtained has a relatively large convergence domain due to the approach function compared with the Taylor series, which makes the series solution independent of random parameters with small fluctuation. Further, a dimension reduction strategy is proposed to improve the computational efficiency of the solution. The numerical examples show that:when considering the computational accuracy, compared with the recently widely used generalized polynomial chaos method (GPC), a third-order expansion of the proposed method is comparable with the second-order expansion of GPC, a sixth-order expansion of the proposed method is comparable with the fourth-order expansion of GPC. However, the computational effort of the former is significantly less than the latter. In addition, the presented method are also suitable for solving geometric nonlinearity problems.