Penetration resistance is an essential design requirement for fiber reinforced polymer (FRP) composites. Furthermore, the penetration energy of FRP composites is known to be sensitive to the indenter nose shape. This gives a challenge for understanding the composite failure mechanisms, as the target plate deformation and energy absorption capacity vary significantly from one indenter to another. The present work is intended to explore the indenter nose shape sensitivity of quasi-static punch shear behavior of glass/epoxy and different weight percentages (0%, 2%, 4%, 6% and 8%) of nanoclay/glass/epoxy composites. A series of punch-shear experiments with different indenter geometries (conical, elliptical, flat and hemispherical) and tensile tests are performed. The results show that the indentation time and energy absorption are more when the flat indenter passes through the laminates which lead to disc mode shape failure whereas conical indenter penetrates rapidly which is attributed to the lower contact surface as compared to the other indenters. The elliptical indenter generates more friction energy and causes the bulge shape damage. The optimum clay content is experimentally studied which improves the punch resistance. It is also examined that the tensile strength and stiffness increase and the percentage of failure strain decreases with the clay effect.