This paper addresses the issue of performing global sensitivity analysis of model output with dependent inputs. First, we define variance-based sensi- tivity indices that allow for distinguishing the independent contributions of the inputs to the response variance from their mutual dependent contribu- tions. Then, two sampling strategies are proposed for their non-parametric, numerical estimation. This approach allows us to estimate the sensitivity indices not only for individual inputs but also for groups of inputs. After testing the accuracy of the non-parametric method on some analytical test functions, the approach is employed to assess the importance of dependent inputs on a computer model for the migration of radioactive substances in the geosphere.