The concept of using continuous filaments (threads) to reinforce soils has been applied in practice for more than a decade. The design of soil structures reinforced with continuous thread is based on limit state techniques  where the failure criterion of the composite is the essential function. This paper is focused on deriving such a function. A homogenization technique is used to calculate the components of the macroscopic stress state at  failure. The limit condition is anisotropic because of the preferred plane of the filament deposition. In the stress space used here the limit condition has the shape of a convex cone with a cross section close to that of a circle. The numerically derived function gives reasonable estimates of the increase in strength (apparent cohesion) of granular materials reinforced with continuous threads. Further work needs to concentrate on a more accurate description of the stress mobilization in filaments during failure, and on including the filament-matrix
slip. The numerically calculated failure criterion has a form convenient for use in stability analyses of structures.