Computational modeling can provide insight into understanding the damage mechanisms of soft biological tissues. Our gradient‐enhanced damage model presented in a previous publication has shown advantages in considering the internal length scales and in satisfying mesh independence for simulating damage, growth and remodeling processes. Performing sensitivity analyses for this model is an essential step towards applications involving uncertain patient‐specific data. In this paper, a numerical analysis approach is developed. For that we integrate two existing methods, that is, the gradient‐enhanced damage model and the surrogate model‐based probability analysis. To increase the computational efficiency of the Monte Carlo method in uncertainty propagation for the nonlinear hyperelastic damage analysis, the surrogate model based on Legendre polynomial series is employed to replace the direct FEM solutions, and the sparse grid collocation method (SGCM) is adopted for setting the collocation points to further reduce the computational cost in training the surrogate model. The effectiveness of the proposed approach is illustrated by two numerical examples, including an application of artery dilatation mimicking to the clinical problem of balloon angioplasty.