During magnetic pulsed welding (MPW), a wavy interface pattern can be observed. However, this depends on the specific material combination being joined. Some combinations, e.g., steel to aluminum, simply provide undulating waves, while others, e.g., titanium to copper, provide elegant vortices. These physical features can affect the strength of the joint produced, and thus a more comprehensive understanding of the material combination effects during MPW is required. To investigate the interfacial morphology and parent material properties dependency during MPW, tubular Al1100 and various copper alloy joints were fabricated. The influence of two material properties, i.e., yield strength and density, were studied, and the interface morphology features were visually investigated. Results showed that both material properties affected the interface morphology. Explicitly, decreasing yield strength (Cu101 and Cu110) led to a wavy interface, and decreasing density (Cu110 and CP-Ti) resulted in a wave interface with a larger wavelength. Numerical analyses were also conducted in LS-DYNA and validated the interface morphologies observed experimentally. These simulations show that the effect on shear stresses in the material is the cause of the interface morphology variations obtained. The results from this research provide a better fundamental understanding of MPW phenomena with respect to the effect of material properties and thus how to design an effective MPW application.