The natural laminar and stable heat and mass convection in an enclosure defined by two horizontal confocal elliptical cylinders with normal and opposite buoyancy forces under uniform concentration and temperature has been numerically explored in this study. The physical Cartesian domain is transformed into an elliptical domain. For the numerical simulation, the equations of conservation of mass, momentum and energy as well as the boundary conditions are discretized by the numerical approach of finite volumes. The algebraic equations obtained were solved by the iterative Gauss-Seidel method. As a function of the effective variables, which are the Rayleigh number, the buoyancy force number N, the Prandtl number, and the Lewis number, the findings are shown as fields of velocities, temperatures, and concentrations as well as the average Nusselt and Sherwood numbers. The results showed that there is a critical buoyancy ratio Ncr = −1, where the mean Sherwood and Nusselt number values are minimal. Their values are decreased by rising values of N when N < Ncr and raised by rising values of N when N > Ncr, and raising the buoyancy ratio N's absolute value results in higher heat and mass transfer characteristics (averages Nusselt and Sherwood numbers).