The pathophysiology of atherosclerotic lesions, including plaque rupture triggered by mechanical failure of the vessel wall, depends directly on the plaque morphology-modulated mechanical response. The complex interplay between lesion morphology and structural behaviour can be studied with high-fidelity computational modelling. However, construction of three-dimensional (3D) and heterogeneous models is challenging, with most previous work focusing on two-dimensional geometries or on single-material lesion compositions. Addressing these limitations, we here present a semi-automatic computational platform, leveraging clinical optical coherence tomography images to effectively reconstruct a 3D patient-specific multi-material model of atherosclerotic plaques, for which the mechanical response is obtained by structural finite-element simulations. To demonstrate the importance of including multi-material plaque components when recovering the mechanical response, a computational case study was conducted in which systematic variation of the intraplaque lipid and calcium was performed. The study demonstrated that the inclusion of various tissue components greatly affected the lesion mechanical response, illustrating the importance of multi-material formulations. This platform accordingly provides a viable foundation for studying how plaque micro-morphology affects plaque mechanical response, allowing for patient-specific assessments and extension into clinically relevant patient cohorts.