The aim of this thesis was to study the load bearing capacity of anchor plates, used for anchorage to concrete located at nuclear facilities. Two different type of anchor plates were examined, which together constitute the majority of the anchor plates used at Forsmark nuclear facility in Sweden. The first is a cast-in-place anchor plate with headed studs and the second is a post-installed anchor plate which uses sleevetype expansion anchors. Hence, anchors with both a mechanical or a frictional interlock to the concrete were examined. The main analysis tool was the finite element method, through the use of the two commercially available software packages ABAQUS and ADINA and their non-linear material models for concrete and steel. As a first step, the numerical methods were verified against experimental results from the literature. However, these only concern single anchors. The results from the verifications were then used to build the finite element models of the anchor plates. These were then subjected to different load combinations with the purpose to find the ultimate load capacity. Failure loads from the finite element analyses were then compared to the corresponding loads calculated according to the new European technical specification SIS-CEN/TS 1992-4 (2009). Most of the failure loads from the numerical analyses were higher than the loads obtained from the technical specification, although in some cases the numerical results were lower than the technical specification value. However, many conservative assumptions regarding the finite element models were made, hence there might still be an overcapacity present. All analyses that underestimate the failure load were limited to large and slender anchor plates, which exhibit an extensive bending of the steel plate. The bending of the steel plate induce shear forces on the anchors, which leads to a lower tensile capacity. In design codes, which assume rigid steel plates, this phenomenon is neglected. The failure loads from all different load combinations analysed were then used to develop failure envelopes as a demonstration of a useful technique, which can be utilised in the design process of complex load cases.