Cardiovascular diseases continue to be the primary cause of death worldwide, where the buildup of plaque within arterial walls, known as atherosclerosis, is a major contributor to various acute cardiovascular events. Determining the material properties and the resulting stress distributions is crucial in the risk assessment of atherosclerotic plaques, as stress is considered an indicator of plaque vulnerability. Material models can be found with stress-strain pairs, but experimentally determining stress tensors is challenging. To address this limitation, we use a recently developed technique called EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) for material characterisation of a two-dimensional multicomponent atherosclerotic plaque, based solely on displacement and force data. A finite element model was developed to simulate the mechanical behaviour of the plaque using the neo-Hookean hyperelastic model, and noisy data was introduced into the model by applying Gaussian noise on the displacements. An L-BFGS gradient descent optimiser was used to minimise the objective function, which is the residual error between predicted internal forces and true external forces. Results showed that at the expected noise level in clinical imaging modalities, no physically relevant stress distributions were obtained, where the plaque’s heterogeneity was observed to affect the accuracy. Clinical imaging was further emulated by systematically removing data to determine the effect of missing data on the model. No significant deterioration of the accuracy of obtained parameters was seen until using 10% of the total data, indicating good robustness to missing data. While the study has limitations, the proposed approach could have implications for the future diagnosis and treatment of atherosclerosis. Future research could explore alternative optimisation algorithms or techniques to improve the model’s accuracy under these conditions.