The low velocity impact (LVI)-induced damage of a highly anisotropic laminate [0/90/0/909]s has been studied experimentally and numerically. The purpose of the analyses of this laminate is that this stacking sequence resembles a sandwich composite panel, in the sense that the [0/90/0] outer layers serve as the “face sheet” while the inner 18 plies of 90 deg layers serve as the “core.” The LVI-induced damage pattern of this laminate is unique and referred to as the “kidney” shape. The “kidney” shape damage is caused by a strong interaction between matrix transverse cracking and delamination, hence is challenging to be computationally captured. The enhanced Schapery theory (EST) model has been improved with the capability to model material inelasticity, as well as a novel mixed-mode cohesive law, to tackle this problem. EST with inelasticity (EST-InELA) is shown to be able to predict load responses and damage morphology accurately and efficiently. The aim of this paper is to provide a challenging LVI case to examine and calibrate computational models.