Quantifying biomechanical properties of atherosclerotic plaques may help preventing strokes. Non-invasive vascular elastography (NIVE) in superficial carotid arteries has the potential to assess such properties and to discriminate plaque components (e.g., fibrosis, lipid and calcium) through elastograms (i.e., spatial strain distribution). However, the elasticity and morphology of the vessel wall, cannot be assessed directly from strain maps since the stress distribution remains unknown. In this study, we describe an unsupervised inverse problem for elasticity mapping (non invasive vascular modulography), which is capable of reconstructing a heterogeneous Young's modulus distribution of a plaque. High resolution elastograms were computed from ultrasound compounded plane wave images using the constrained lagrangian speckle model estimator (constrained LSME). Von mises strain maps were combined with a stress map, evaluated using a parametric finite element model (PFEM), and used to highlight mechanical heterogeneities and compute Young modulus maps (Modulograms).