In this study (Part I), an advanced empirical formulation was proposed to predict the ultimate strength of initially deflected steel plate subjected to longitudinal compression. An advanced empirical formulation was proposed by adopting Initial Deflection Index (IDI) concept for plate element which is a function of plate slenderness ratio (β) and coefficient of initial deflection. In case of initial deflection, buckling mode shape, which is mostly assumed type in the ships and offshore industry, was adopted. For the numerical simulation by ANSYS nonlinear finite element method (NLFEM), with a total of seven hundred 700 plate scenarios, including the combination of one hundred (100) cases of plate slenderness ratios with seven (7) representative initial deflection coefficients, were selected based on obtained probability density distributions of plate element from collected commercial ships. The obtained empirical formulation showed good agreement (R2 = 0.99) with numerical simulation results. The obtained outcome with proposed procedure will be very useful in predicting the ultimate strength performance of plate element subjected to longitudinal compression. Copyright © 2018 Techno-Press, Ltd.