For the assessment of existing masonry structures, a safety concept is required that takes into account the differences compared to the design of new masonry structures, such as the possibility of material testing, high variability of material properties, and a potentially reduced target reliability level. Therefore, a method for determining characteristic values, structure-specific partial factors, and assessment values for the compressive strength of existing masonry is developed. For this purpose, the influence of spatially variable material properties within a masonry wall is investigated first: Based on experiments on clay brick masonry, a finite element model is developed and then used in Monte Carlo simulations for quantifying the effect of spatial material variability on the probability distribution of the load-bearing capacity of masonry walls under compression. The statistical uncertainty resulting from small sample sizes in material testing is considered through Bayesian statistical procedures. Prior distributions for unit, mortar, and masonry compressive strength are modelled utilising a test database for existing solid clay brick masonry. Finally, the findings are implemented in a practice-oriented method for determining assessment values of masonry compressive strength, which is validated through reliability analyses.