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Elastoresistance is the relative change of a material’s resistance under strain. Its value depends on two contributions: one coming from changes in the sample’s geometry and another from changes of the electronic properties such as carrier densities or scatering rates. In common metals like copper, the geometric contribution dominates a temperature-independent elastoresistance with a value of about 2. In other materials, including Bi, changes in the electronic properties dominate. We find that WTe₂ is a member of the second group exhibiting an elastoresistance as large as -20. Moreover, we discover that the magnetic field has a dramatic effect on the elastoresistance in WTe₂, resulting in values of elastoresistance in applied magnetic field between -80 to 120. We present a detailed analysis of this phenomenon combining results from DFT calculations and quantum oscillation measurements. We conclude that such large magneto-elastoresistance can be realized in other semi-metals with crystal structures similar to WTe₂.