Different low-permeability formations are considered as potential host rocks for Low / Intermediate Level waste (L/ILW) and spent fuel / high-level / long-lived intermediate-level waste (SF/HLW/ILW) in Switzerland. As part of a generic site evaluation process, emphasis is on the assessment of Mesozoic limestones, marls and claystones in six potential siting areas in Northern and Central Switzerland. An important aspect in the site evaluation process is the characterization of the low-permeability formations in terms of spatial variability of the relevant transport properties (porosity, permeability, clay content), as they may affect the migration of waste-generated gas from L/ILW and SF/HLW/ILW repositories. Numerical modeling studies are presented, aimed at quantifying the impact of spatial variability of rock properties on gas release through the host rock on a deca- to hectometer scale. For this purpose, 2D models of an emplacement tunnel embedded in a low-permeability host rock are developed for both a sequence of limestones and marls with distinct lithological variability (Effingen Beds) and a claystone of moderate spatial variability (Opalinus Clay). For the Effingen Beds, a composite geological model is implemented, comprising stochastic representations of the different facies and the fracture systems. The facies model displays spatial variations in clay content, porosity and permeability within the different facies. The fracture model accounts for the hydraulic effects associated with the faults and fracture systems in the siting area under consideration. For the Opalinus Clay the available geostatistical information (experimental variograms of clay content, porosity, hydraulic conductivity) is used to generate a stochastic facies model based on a log-normal permeability distribution. A separate fracture network model is not established for the Opalinus Clay. A generic gas source-term is assigned to the emplacement tunnel and hydrostatic pressures are initially assumed for the host-rock domain. The comparison of the simulations with different permeability realizations indicates that the heterogeneity of the host rock introduces strong differences in the propagation of the gas pressure perturbation, resulting in significant variations in the lateral propagation of the gas front in the host rock and the gas pressure build-up in the emplacement tunnels. Despite these differences, the calculated peak pressures in the disposal cavern and gas breakthrough along the upper model boundary are similar for multiple realizations, which compare well with the simulated results for a homogeneous model with equivalent averaged properties.