Electrification of mobility highlights the need for highly digitalized and adaptable welding technologies. Laser welding comes as an essential solution for this emerging sector, especially in the production of battery systems, drive trains, and lightweight body in white. Contemporary fiber laser generations with flexible beam shaping solutions consisting of a core complemented with a coaxial ring are ideal for such applications. On the other hand, the added flexibility of the new beam shapes generates a wider parameter space for process development. Analytical modelling tools can be of aid for parameter screening purposes if adequately calibrated and validated. However, analytical solutions to model the thermal field in laser welding generated by a core and ring configuration are still to be generated. Hence, in this work an analytical model is introduced to model the laser welding with a single-mode Gaussian core with an external ring profiles. A combination of a Gaussian and a toroidal volumetric heat sources was proposed to represent the core and ring beams, respectively. Consequently, the mathematical development was calibrated and validated with bead on plate experiments conducted on 5 mm thick EN AW-1050 alloy using a fiber laser with separate control of the power content within the single mode core and the ring portions of the beam.