This document presents results from a numerical study of the progressive damage capabilities of the MAT162 material model in Ls-DYNA explicit finite element code. Single-shear fastener lap joint of multi-directional laminates made of AS4/3501-6 carbon/epoxy unitape plies were used in the study. MAT162 is a progressive damage model which utilizes Hashin failure criteria to evaluate damage initiation and progression in fabric and unidirectional composite plies. [45/-45/0/90]2S, [45/0/-45/90]2S and [30/-30/0/90]2S laminates have been investigated in this study. The analysis included unnotched, open-hole and single-shear lap joints using fasteners. Remote stress-strain curves, damage initiation and damage progression are presented for all the analyzed cases. The analyses indicate matrix cracking as the damage initiator at off-axis ply interfaces in [45/-45/0/90]2S, [45/0/-45/90]2S and [30/-30/0/90]2S laminates. Matrix cracking propagation led to delamination at the 0 degree/90 degree interface. The load transferred through the fastener was 30% for the [45/-45/0/90]2S and [45/0/-45/90]2S laminates and 25% for the [30/-30/0/90]2S laminate. Brittle net section failure was the failure mode identified in all the analyzed specimens, which agrees with previous experimental work carried out by several authors