Significant interest has recently focused on the use of liquid-metal targets flowing with high velocities for various high-power nuclear and high-energy physics applications such as fusion reactor first-walls, the Spallation Neutron Source, Isotope Separation On Line, and Muon Collider projects. This is because the heat generated in solid targets due to beam or plasma bombardment cannot be removed easily and the resulting thermal shock damage could be a serious lifetime problem for long-term operation. More recently, the use of free or open flying-liquid jets has been proposed for higher-power-density applications. The behavior of a free-moving liquid mercury or gallium jet subjected to proton beam deposition in a strong magnetic field has been modeled and analyzed for the Muon Collider project. Free-liquid-metal jets can offer significant advantages over conventional solid targets, particularly for the more demanding and challenging high-power applications. However, the use of free-moving liquid-metal targets raises a number of new and challenging problems such as instabilities of the jet in a strong magnetic field, induced eddy-current effects on jet shape, thermal-shock formation, and possible jet fragmentation. Problems associated with shock heating of liquid jets in a strong magnetic field are analyzed in this study.