Quantitative mechanical properties of biological tissues can be mapped using the shear wave elastography technique. This technology has demonstrated a great potential in various organs but shows a limit due to wave attenuation in biological tissues. An option to overcome the inherent loss in shear wave magnitude along the propagation pathway may be to stimulate tissues closer to regions of interest using alternative motion generation techniques. The present study investigated the feasibility of generating shear waves by applying a Lorentz force directly to tissue mimicking samples for magnetic resonance elastography applications. This was done by combining an electrical current with the strong magnetic field of a clinical MRI scanner. The Local Frequency Estimation method was used to assess the real value of the shear modulus of tested phantoms from Lorentz force induced motion. Finite elements modeling of reported experiments showed a consistent behavior but featured wavelengths larger than measured ones. Results suggest the feasibility of a magnetic resonance elastography technique based on the Lorentz force to produce an shear wave source.