Abstract: It is of great importance to incorporate uncertainties intostructural topology optimization problems. Based on the definition of thenon-probabilistic reliability index, this paper proposes a mathematicalmodel for topology optimization of 3D continuum structures withnon-probabilistic reliability constraints on deformation. In this model,the uncertainties in material properties, geometrical dimensionsand loading conditions are accounted for. The Performance Measure Approach(PMA) is adopted for transformation of the constraints. In this context, theadjoint variable scheme for sensitivity analysis of the target performanceis discussed, which facilitates a mathematical programming solution of theoptimization problem. Numerical investigations illustrate the applicabilityand the validity of the present model as well as the proposednumerical techniques. The computational results show thatnon-probabilistic reliability-based topology optimization may yield morereasonable material layouts than the conventional deterministic approach.