Creep specimens prepared of magnesium alloy AE42 were investigated under constant load in compressive and in tensile creep. Material was cast via the squeeze casting process in order to obtain a dense microstructure without pores. Creep tests were performed at constant temperatures between 150 °C and 240 °C and constant applied stresses between 40 MPa and 120 MPa until a minimum creep rate was reached. It could be seen that the minimum creep rates in compressive creep tests were smaller than in tensile creep tests, and the difference increased with increasing applied stress. Stress exponents were determined according to the Norton equation and it was found that a threshold stress had to be introduced into the analysis. The threshold stress is based on strengthening by aluminum-rare earths precipitates. Calculating the true stress exponent, deformation mechanisms during creep could be clarified.