The investigations have demonstrated that variations in masonry unit height influence the load-bearing behaviour of DSM walls. Deviations in height generate local gaps that induce tilting and seating effects, alter load distribution and progressively improve contact areas under increasing loading. The second dominant parameter is wall slenderness: increasing slenderness significantly reduces both the mean and the characteristic compressive capacity due to second-order effects. The resulting capacity reduction factor in slenderness is highly nonlinear, particularly when geometric imperfections are pronounced. Models that neglect the interaction between height imperfections and slenderness substantially predict compressive strength incorrectly. Surface roughness has only a minor influence on mean capacity, but it increases dispersion of results and prediction uncertainty. Despite height imperfections, load transfer at peak load resembles that of ideally aligned walls, while failure is governed by local masonry fracture and contact failure. Based on these findings, a design model for concentric axial loading was developed as a function of wall slenderness. This model incorporates a partial safety factor to reflect statistical uncertainty and a nonlinear factor to account for geometric variability. In the first study phase, 218 finite element (FE) simulations were conducted to assess the effects of slenderness and roughness. The second phase involved performing 500 nonlinear FE simulations, each including up to 300,000 deformable elements, using Abaqus/Explicit on HPC systems, to investigate the combined effects of slenderness and eccentricity. The results show that loading eccentricity has a significant impact on capacity. For reference models with perfect contact, an eccentricity ratio of e/t = 0.40 reduces compressive strength by up to 50% compared to that of DSM wall under axial loading. This reduction persists across all slenderness levels when stochastic height imperfections are included. Eccentric loading induces out-of-plane bending, uplift of one face shell and elevated tensile and shear stresses. This leads to failure that is governed by tensile cracking, diagonal compressive damage and instability. While initial load transfer occurs through discrete contact zones, seating and tilting progressively form more distributed load paths. Across all stochastic realisations, compressive strength decreases almost linearly for the investigate range between 0.15 and 0.40. For each slenderness–eccentricity combination, strength distributions were probabilistically evaluated. Despite a unit height coefficient of variation (CoV) of only 0.3%, wall strength exhibits a CoV of 10–13%, highlighting the strong amplification of geometric imperfections. Normal distributions best fit the FE results and provide slightly conservative characteristic values. A reduction factor, ϕ, dependent on slenderness and eccentricity, was derived and integrated into a design formulation analogous to DIN EN 1996-1-1. The proposed approach predicts characteristic capacities that are 40–76% lower than those of simplified models without distribution of height imperfection. Validation against experiments in the literatures eccentrically loaded DSM walls confirms the method's accuracy and consistency when combined with an appropriate partial safety factor. In summary, variability in unit height, wall slenderness and loading eccentricity interact strongly and must be considered simultaneously. Probabilistic modelling is essential in order to capture these nonlinear effects, and the proposed stochastic finite element (FE) framework provides a robust basis for the reliable prediction of strength and the design of DSM walls under eccentric compression.