Temperature, plastic strain and heat generation during the plunge stage of the friction stir welding of high-strength aluminum alloys 2024 T3 and 2024 T351 are considered in this work. The plunging of the tool into the material is done at different rotating speeds. A 3-D finite element model for thermomechanical simulation is developed. It is based on arbitrary Lagrangian-Eulerian formulation, and Johnson-Cook material law is used for modelling of material behaviour. From comparison of the numerical results for alloys 2024 T3 and 2024 T351, it can be seen that the former has more intensive heat generation from the plastic deformation, due to its higher strength. Friction heat generation is only slightly different for the two alloys. Therefore, temperatures in the working plate are higher in the alloy 2024 T3 for the same parameters of the plunge stage. Equivalent plastic strain is higher for 2024 T351 alloy, and the highest values are determined under the tool shoulder and around the tool pin. For the alloy 2024 T3, equivalent plastic strain is the highest in the influence zone of the tool pin.