In this paper we define a multi-scale distance between shapes based on geodesics in the shape space. The proposed distance, robust to outliers, uses shape matching to compare shapes locally. The multi-scale analysis is introduced in order to address local and global variabilities. The resulting similarity measure is invariant to translation, rotation and scaling independently of constraints or landmarks, but constraints can be added to the approach formulation when needed. An evaluation of the proposed approach is reported for shape classification and shape retrieval on the part B of the MPEG-7 shape database. The proposed approach is shown to significantly outperform previous works and reaches 89.05% of retrieval accuracy and 98.86% of correct classification rate.