The composite material comprises a biocompatible titanium (Ti) or biocompatible Ti alloy, and biodegradable component, which is intended to at least partially desorb in vivo in contact with human tissue and which has an Young's elastic modulus lower than used Ti or Ti alloy. The material is prepared from a mixture of the particles of Ti or Ti alloy and the particles of the biodegradable component, wherein the biodegradable component, in particular magnesium (Mg), is dispersed throughout a volume of the material and occupies 2 to 20 volumic % in the material. The biodegradable component is present in a bearing Ti or Ti alloy structure in the form of filaments oriented along an extrusion axis. A manufacturing process comprises fabrication of powders, mechanical blending of powders to a homogeneous mixture and a subsequent extrusion at a temperature from 300 °C to 640 °C. The components are consolidated to a common mass, wherein during a consolidation the biodegradable component is formed into filaments oriented along an extrusion direction. Prior heated and extrusion the powder mixture may be precompacted in order to reach acceptable handling strength and cohesion.