In this paper, a mechanical model consistent with the main assumptions of the Critical Shear Crack Theory (CSCT) is proposed for shear design of slender concrete members without shear reinforcement. To that aim, the shear force that can be transferred through the critical shear crack by aggregate interlock, residual tensile strength and dowelling action as well as due to the inclination of the compression chord are calculated by integration of fundamental constitutive laws accounting for the critical shear crack opening and kinematics at failure. The pertinence of the assumptions is validated through comparisons to detailed test measurements to assess their validity. The model allows predicting the failure load, the deformation capacity and the location of the critical shear crack leading to failure. The results are checked against large datasets and the model is finally used to discuss on the influence of the various parameters on the governing shear-transfer actions. The results are eventually used to propose improvements on the CSCT failure criterion for shear, relating the shear strength and its associated deformation capacity.