Mechanical characterization of individual microstructural phases of hardly deformable magnesium alloys is of crucial importance for the development of multi-scale material models. The magnesium alloys are used for preparation of fine tubes with diameter of a few millimeters and tens of millimeters wall thickness. It is hard to control an ordinary drawing process for the preparation of such tubes. However, the tubes can be prepared with a laser dieless drawing process that is, in contrary to conventional drawing, able to draw low formability materials and it is able to produce variable cross-sections of the tube or a wire with high precision. The magnesium alloy tubes are used in various fields as micro-electro-mechanical systems, medicine, electrical, biological and chemical fields. In this paper, preliminary microstructural studies and local mechanical characterization of pure Mg, MgCa0.8 and AZ31 magnesium alloys used for tube extrusion, is provided. The material microstructure is studied by means of scanning electron, atomic force microscopes and nanoindentation. Elastic properties and volume fractions of mechanically distinct phases that are not accessible by standard testing methods are provided in the paper.