This paper presents a theoretical study of failure modes in sand-like granular materials under general triaxial stress conditions based on a hypoplastic model and a bifurcation analysis. The well developed constitutive model contains the void ratio as a state variable which allows the pressure and density dependent behaviour of the granular materials to be described with a single set of state-independent constitutive parameters. Based on this model a shear bifurcation condition is derived. Loading along various stress paths that can be achieved with a true triaxial test apparatus are simulated numerically. Either localized failure or uniform diffuse failure in granular samples may occur, which is determined based on whether the shear bifurcation condition is met. Effects of confining pressure and initial density are discussed.