Summary: This paper develops an unstructured solution algorithm for the computation of compressible Reynolds-averaged Navier-Stokes (RANS) equations using turbulence models. An algebraic turbulence model based on the Baldwin and Lomax model (BLM) and a one-equation Baldwin and Barth model (BBM) have been implemented on fully unstructured meshes. The eddy viscosity is computed using the BLM along turbulence stations normal to the wall. For each turbulence station a number of turbulence sample points are generated. These sample points are used to gather the information required for computing the eddy viscosity. For each time-step, the current flow variables are interpolated from the unstructured mesh onto the turbulence sample points. The BLM is evaluated on the turbulence stations and the resulting eddy viscosity values are stored at each sample point and then interpolated back to the mesh. The alternating digital tree data structure is used to increase the efficiency of the searching for the element in the mesh that contains the sampling point. The implementation of BBM is using a Galerkin finite element approximation with an edge-based data structure. The integration in time of BBM is performed explicitly by the use of a Runge-Kutta multi-stage method. These models are validated using an efficient, unstructured, multigrid finite element Navier-Stokes solver, by comparing the computed results with available theoretical and experimental results.