Numerical analyses have shown that successful flow simulations and the accuracy of solution noticeably depend on the number of nodes used in computational meshing. A suitable meshing should have the capability of adapting with main flow parameters. Because the number of total nodes that can be used in numerical simulation is limited, making such grid for complex flows is almost difficult, if it is not impossible. Also, the regions of large solution gradients are not defined at the beginning. So using adaptive meshing in numerical solving methods is desired. Among adaptive meshing methods, adaptive-grid redistribution and embedding methods have been considered more by researchers. Combination of these two methods is more complex than each one alone. For the purpose of analyzing the accuracy and the efficiency of solution, the combination is used for solving two dimensional Euler equations in two model problems. The results show that using combination of adaptive-grid redistribution and embedding methods requires less nodes and therefore less memory and computation time. Therefore combination of this adaptive meshing is suitable.