The carbuncle phenomenon, commonly occurring in solutions of compressible Euler equations, is a numerical instability associated with shock-induced anomalies. It is associated with several shock-capturing finite-volume methods designed to preserve the contact discontinuities. Due to the lack of theoretical knowledge of the carbuncle phenomenon, it is not known which numerical scheme is affected or under what circumstances that the phenomenon occur. The objective of this article is to study the numerical instability of advection upstream splitting method (AUSM) family schemes so called the AUSMD, AUSMV and AUSMDV schemes in two-dimensional structured triangular grids by examining the shock-induced anomalies produced by these original schemes in different test cases. A multidimensional dissipation technique is proposed for these schemes. The evolution of perturbations is also studied by means of a linearized discrete analysis to the odd–even decoupling problem. The recursive equations show that the AUSMDV-family schemes with the dissipation technique are less sensitive to these anomalies than the original schemes. Finally, the dissipation technique is extended to the second-order schemes and tested by several test cases.