A computational finite-volume scheme, based on the structured-grid multi-block approach and incorporating a new variant from the group of low-Reynolds-number k — ϵ models, is applied to the transitional flow in a 3D turbine cascade. The turbulence model is designed, by reference to a particular one-equation model, to give the correct variation of turbulence length scale as the wall is approached. Its performance characteristics are first demonstrated through calculations for a transitional flat-plate boundary layer, prior to its application to the 3D turbine cascade. The characteristics of the cascade flow are examined in detail, especially in terms of the structure of the passage vortex and losses arising from turbulence. The latter are shown to be over-estimated relative to the experimental levels due to a premature onset of transition in the blade's boundary layers, especially near the end wall.