The Buckmaster equation, integral to the study of flat fluid plates and their substantial deformation and dynamics, has long intrigued researchers. Despite this, its complexity has confined solution attempts to numerical methods, leaving a gap for an analytical approach. Addressing this challenge, our study applies the Elzaki Projected Differential Transform Method (EPDTM), which is a semi-analytic method, to the nonlinear partial differential Buckmaster equation. This innovative method stands out from previous numerical attempts with its precision, efficiency, and minimal computational demand. Through the EPDTM, we present approximate solutions for two specific cases and extend our analysis to the general form of the Buckmaster equation. Comparative visualizations against the exact solutions, supplemented by tabular and graphical analyses, confirm the negligibility of absolute errors. Crucially, convergence plots verify the EPDTM’s efficacy, showcasing the solutions’ progressive alignment with the exact solution. This study not only demonstrates the EPDTM’s potential in solving complex equations with greater simplicity and speed but also opens avenues for its application in broader mathematical and scientific disciplines.