The paper evaluates the performance of alternating current (AC) square waveform submerged arc welding (SAW) as a candidate technology for manufacturing thick welds for high-pressure vessels. A new mathematical formulation for calculating melting efficiency in square waveform arc welding is presented. The melting efficiency and the heat consumption are presented as a mathematical model of welding parameters, namely welding current, welding speed, current frequency, and electrode negativity (EN) ratio. The proposed approach is demonstrated through the welding of 2.25Cr-1Mo heat-resistant steel performed over a wide range of welding parameters. The investigation provides deeper insights into the interplay between process parameter, total heat consumption, and melting efficiency. The effect on flux consumption is also explained. The melting efficiency is inversely proportional to flux consumption. The welding heat does not necessarily promote the plate melting. Improper use of welding heat may lead to decreased melting efficiency and increased unwanted melting and consumption of welding flux. Compared to the conventional direct current (DC) power sources, the AC square waveform welding achieves almost the same order of melting efficiency with added advantages of better weld bead shape and flux consumption in a desirable range. The two additional parameters (frequency and EN ratio) of the AC square waveform power source provide more freedom to fine-tune the process and thereby efficiently use welding heat. The results of this investigation will be advantageous to the designers and fabricators of high-pressure vessels using AC square waveform welding.