This study presents a model for Ti6Al4V alloy produced by applying electron beam melting as continuum media with orthotropic elastic and plastic properties and its application in total hip replacement (THR). The model exhibits three Young’s moduli, three shear moduli, and three Poisson’s ratios as elastic properties and six coefficients describing the Hill yield criterion. Several uniaxial tension and torsion experiments and subsequent data processing were performed to evaluate the properties and coefficients. The typical values obtained for Young’s moduli, shear moduli, and Poisson’s ratio were 121–124 MPa, 37–42 MPa, and 0.25–0.26, respectively. A comparison of the experimental tension and torsion curves with those obtained by a finite element analysis revealed a good correlation with a maximum error of 9.5%. The finite element simulation of a personalised pelvic implant for THR manufactured from the obtained material proved the mechanical capability of the implant to successfully withstand the applied loads.