This paper investigates the influence of damping on dynamic punching shear assessment, focusing on the case of sudden column removal in buildings. It advances an existing dynamic punching shear model developed at the University of Surrey, by incorporating the damping effect on dynamic amplifications. Specifically, the dynamic displacement amplification factor is analytically evaluated through basic principles, by assuming a parabolic load-rotation curve and fluid viscous damping properties. Accordingly, the damping effect is also explicitly considered in the dynamic load amplification factor, thus providing a more realistic estimate of the punching shear demand in column removal situations. The proposed model is applied in a flat slab reinforced concrete building that can be considered as representative of residential and commercial buildings. It is shown that for common damping levels encountered in practice, the dynamic punching shear demand-to-capacity ratio decreases slightly with increasing damping ratio. Hence, in these cases, the damping effects can be conservatively disregarded from calculations. Overall, the proposed model offers a simple, yet reliable, method to account for damping when assessing the safety against punching due to sudden column removal scenarios.