The paper presents a detailed theoretical analysis of the electromagnetic forces in the arc plasma and the weld pool metal in Tungsten Inert Gas (TIG) welding at direct current (DC) and high-frequency pulse current (HFPC) modulation with a frequency of 10 kHz. The electromagnetic (Lorentz) force, acting on arc plasma and metal is presented via potential (magnetic pressure) and rotational (equivalent electromagnetic force) force components. This approach allows us to substantially simplify the analysis of the Lorentz force effect on the arc plasma and weld pool metal under different arc burning modes. It was shown that in HFPC TIG welding with a given frequency, the effect of modulated current on the arc plasma is inherently non-stationary, whereas the effect on the weld pool metal is determined by the time-averaged magnitude of electromagnetic force throughout the period of current modulation. The proposed approach serves as a basis for numerical analysis of the electromagnetic forces in arc plasma and weld pool metal during DC and HFPC modes of the welding process. We established that the application of HFPC modulation promotes a greater intensity of both the gas-dynamic processes in the welding arc, thereby significantly increasing the pressure on the weld pool surface, and convective heat transfer from the most heated central region near the weld pool surface towards the weld pool bottom. Both these factors lead to an increase of the arc penetrability in the case of the HFPC mode compared with the DC mode, all other conditions being equal. •Only rotational part of the Lorentz force initiates vortical flow.•Square-wave pulse is used as a welding current wave form.•Non-stationary magnetic field diffusion equation is solved numerically.•In-house Wolfram Language code is used for FEM-analysis.•HFPC modulation increases the effective driving force in the weld pool.