The tension-compression asymmetry under plastic deformation of cast and extruded AZ31 magnesium alloys was investigated. The cast alloy had a rather random texture, while the extruded alloy had a strong texture in which most of grains have an orientation of their basal planes parallel to the direction of extrusion, namely a basal fiber texture. Uniaxial tension test, uniaxial compression test, and equi-biaxial compression test were performed on both alloys. Based on the results obtained, influences of the deformation pattern and the initial texture on the stress-strain relation and the variation of plastic work were discussed. It was found that the activity of the extension twinning strongly influenced on the stress-strain relations under uniaxial deformations, with regard to the relation between the crystallographic preferred orientation and the loading direction. The comparison of the result under the equi-biaxial compression with that under the uniaxial tension revealed the similarity of mechanical responses, even on strongly textured extruded alloy, owing to the geometrical equivalence on deformation of the specimens. On the other hand, there were clear differences on the fracture stresses as well as the fracture morphologies between the equi-biaxial compression and the uniaxial tension, because of the different fracture mode under compression and tension.