In this paper, the non-Darcy model for natural/mixed convection and heat transfer in a cavity saturated with anisotropic porous media has been investigated using an incompressible smoothed particle hydrodynamics (ISPH) method. In the ISPH algorithm, a semi-implicit velocity correction procedure has been used and the pressure is obtained by solving pressure Poisson equation. The unsteady natural/mixed convection in non-Darcy porous cavities is examined by our extended ISPH method and Finite Volume Method. The results are presented with flow configurations, isotherms and average Nusselt numbers for different Darcy numbers from 10(-4) to 10(-2), porosity values from 0.4 to 0.9, permeability ratio 0.1-10, inclination angle of permeability 0-90 degrees and Reynolds/Rayleigh numbers. The flow pattern and rate of heat transfer inside the cavity are affected by these parameters. The results demonstrate the effects of the parameters such as Darcy number, porosity, permeability ratio and inclination angle in both of the heat transfer rate and the flow regime. The results from this investigation are well validated and have favorable comparisons with previously published results. (C) 2014 Elsevier Ltd. All rights reserved.