A numerical model combining the ultrafast radiative heat transfer and ablation rate equation for free electron density is proposed to investigate the transient process of plasma formation in distilled water. The focused beam propagation governed by the transient equation of radiative heat transfer is solved by the transient discrete ordinates method. The temporal evolution of free electron density governed by the rate equation is solved using a forth-order Runge-Kutta method. Two laser pulses: 30 ps and 300 fs are considered. Simulation of the dynamics of plasma formation is performed. The results include the threshold laser intensity for optical breakdown, temporal evolution and spatial distribution of the free electron density as well as the maximum plasma length. To validate the model, optical breakdown thresholds for different laser pulses, the shape of plasma breakdown region and the maximum plasma length predicted by the present model are also compared with the experimental data.