The aim of the study was the development of models that describe Laser beam welding process of maraging steel 250 sheets, based on measured experimental data. Maraging steel 250 is widely used in applications that require high strength steel. For example, in aerospace industry, to produce engine components, or in sports industry, to produce bicycle frames or golf club heads. In order to achieve a reliable and repeatable welding process, we investigated the influence of welding parameters on the welded process responses, i.e., weld penetration depth and bead width. Two modeling techniques for predicting weld bead geometry were developed and tested. One method is the Multiple Regression Analysis (MRA) which is widely used for modeling welding processes and the other is Artificial Intelligence (AI) technique, which is rarely applied for modeling welding processes. The MRA method uses polynomials to express the relations between bead geometry and welding parameters, while the AI method is more flexible and presents in the model terms with physical meaning. Both MRA and AI models present similar statistical quality of fit between the predicted values of bead geometry and the actual experimentally measured data.