The influence of plasma shielding effect induced by ambient gas pressure and laser intensity on the laser-produced Cu plasma parameters, signal-to-background ratio (S/B) and expansion are experimentally and numerically investigated. A Q-switched Nd:YAG laser at 1064 nm at various intensities ranging from 2 to 7.1 GW/cm2 intensity (40–150 mJ) is used to produce Cu plasma in air, argon (Ar), helium (He), and neon (Ne) ambient gas at various pressures ranging from 5 to 1000 mbar. Laser-induced breakdown spectroscopy reveals that spectral radiation, S/B, electron temperature, number density, and front edge velocity of the plasma have an increasing trend up to a certain value of laser intensity and gas pressure. Afterwards, a saturation trend is achieved, which is attributed to the shielding and self-regulation effect. The numerical modeling of the laser-produced Cu plasma in the presence of air at atmospheric pressure is carried out using the MULTI radiation hydrodynamics code. We have shown that the feature of plasma shielding effect observed in the experiments can be reproduced using a continuum hydrodynamics model. Laser intensity at about 3.5 GW/cm2 is found to produce the highest S/B at 1000 mbar air. He, Ne, air, and Ar show the best S/B, respectively and the best S/B is found for air, Ar, He, and Ne at 10, 5, 10, and 20 mbar, respectively. The expansion of plasma plume is studied using a simple and effective technique based on probe laser absorption and scattering method. The plasma plume expansion through He, Ne, air, and Ar at 1000 mbar pressure has the highest velocity, respectively. The simulated results of strong shock wave model and Rankine–Hugoniot jump condition are fitted to the experimental data, which are then used to estimate the values of the ablation parameters.