The brittleness and the sensitivity to shrinkage cracking of cementitious materials are real handicaps that can limit their durability performance. Enhancing the cracking resistance and strain capacity of cement-based materials is the challenge of broad ongoing research programs. In this regard, the present paper focuses on the design of a mortar exhibiting a high straining capacity before macrocracking localization. It was assumed that the incorporation of aggregates with high deformability could be a solution. Two types of plastic wastes (PET and PC) available in large quantities were used as a partial replacement for natural aggregates in mortar. The experimental results showed that the incorporation of plastic aggregates in cementitious material is a suitable solution to limit its brittleness. Despite the decrease in mechanical strength and the increase of free shrinkage length change, these composites exhibited a considerable improvement of strain capacity and cracking resistance. The plastic aggregates delay shrinkage cracking and cause multiple cracking with smaller crack widths. In addition, mortars containing plastics offer an opportunity to recycle nonbiodegradable wastes.