Plasma-mediated ablation using ultrafast lasers in transparent media such as aqueous tissues is studied. It is postulated that a critical seed free electron density exists due to the multiphoton ionization in order to trigger the avalanche ionization which causes ablation and during the avalanche ionization process the contribution of laser-induced photon ionization is negligible. Based on this assumption, the ablation process can be treated as two separate processes - the multiphoton and avalanche ionizations - at different time stages; so that an analytical solution to the evolution of plasma formation is obtained for the first time. The analysis is applied to plasma-mediated ablation in corneal epithelium and validated via comparison with experimental data available in the literature. The critical seed free-electron density and the time to initiate the avalanche ionization for sub-picosecond laser pulses are analyzed. It is found that the critical seed free-electron density decreases as the pulse width increases, obeying a t(p)(-5.65) rule. This model is further extended to the estimation of crater size in the ablation of tissue-mimic polydimethylsiloxane (PDMS). The results match well with the available experimental measurements. (C) 2012 Elsevier B.V. All rights reserved.