In this work, a method for determining the Equivalent Initial Flaw Size (EIFS) distribution using the Boundary Element Method (BEM) is proposed. Maximum Likelihood Estimation (MLE) is used to infer the EIFS distribution of a cracked stiffened panel under multiple sources of uncertainty, including uncertainty in the loading conditions, fatigue crack growth model parameters, and in the measurement of crack size found from routine inspections. Results suggest that MLE is an effective tool for estimating the parameters of an EIFS distribution when no prior knowledge is available regarding the EIFS distribution or its parameters.