Microchannel fabrication on transparent materials using lasers is difficult for a wide range of wavelength. Laser-Induced Plasma Assisted Ablation (LIPAA) is a novel process for machining of microchannels on the transparent materials. LIPAA overcomes the challenges faced due to its transparency over a wide range of wavelength. Here, transparent materials are ablated with the aid of laser-induced plasma on its rear side. This paper presents a two-dimensional transient numerical model to understand the physics of material removal during the LIPAA process. A realistic model is developed considering assumptions like moving Gaussian heat source, temperature dependent properties and combined convection-radiation effect. Extensive numerical analysis is performed concerning the effect of plasma along with the effect of input laser irradiation. The results predicted have been validated with the experimental results and found in good agreement. The numerical analysis provides some useful observations like increase in pulse power density, pulse repetition rate and pulse duration, enhances the channel dimensions. Similarly, considering the effect of moving heat flux, it is witnessed that the peak temperature attains a constant value on reaching a certain distance, thus assuring a channel of uniform dimension. The developed model can be utilized effectively to establish LIPAA in practice.