Ablative plasma and a shock wave (SW) in ambient air were experimentally produced using Nd:YAG laser pulses of ∼7 ns width and a wavelength of 532 nm. The numerical simulations of the experiments were performed using a two-dimensional axis-symmetric radiation-hydrodynamics code. The numerical approach to simulate the experimental observations was not straightforward due to the complex behavior of the laser-air interaction and the associated processes, such as plasma formation and SW evolution, that occur concurrently. Hence, the modeling was attempted based on the combination of two laser absorption coefficients and two equations-of-state (EOSs). One form of absorption coefficient was taken from Zel'dovich and Raizer [Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover Publications/Academic Press Inc., New York, 2012)], which is the sum of photoionization and inverse bremsstrahlung (IB) due to electron-ion collisions, and the other was taken from DeMichelis [IEEE J. Quantum Electron. 5(4), 188 (1969)] that considers the IB due to electron-ion and electron-neutral collisions. Similarly, the two EOSs, namely the ideal gas EOS and the chemical equilibrium application [S. Gordon and B. J. McBride, NASA Ref. Publ. 1311, 1 (1994)] EOS, are considered. The simulated results obtained using four models were compared with each other and with the experimental observations. These models enabled understanding the transient behavior of the laser-induced air plasma and the SW evolution. The results showed that the absorption coefficient and the EOS play a key role in modeling the dynamics of air plasma and SW. We present the results of this study and the models which validate the experimental results the best in terms of the asymmetric plasma expansion, formation of hot spots, plasma splitting and rolling, SW external dynamics such as the transition from a tear-drop to a spherical shape, and shock front velocity.