Critical plane-based multiaxial fatigue criteria utilize the shear stress amplitude and maximum normal stress to determine whether or not the cyclically loaded component will have infinite fatigue life. The numerical methodology MCC (minimum circumscribed circle), although widely used, has as a limitation the fact that it is not capable of taking into account effects of non-proportionality of the trajectory of the shear stress vector. The MRH method was created to be simpler, and is also a numerical method that, in addition to having lower computational cost, tends to give more conservative results than MCC. In this work, the same 21 loading conditions were used to compare MCC and MRH in obtaining the shear stress amplitude applied to the multiaxial fatigue criteria of Matake, Susmel & Lazzarin, Findley and Carpinteri & Spagnoli, generating tables and graphs in relation to the guidelines of the critical planes obtained, maximum normal stress, shear stress amplitude and error index. For synchronous loading conditions, the analytical method for obtaining the shear stress amplitude was also compared to MCC and MRH. Furthermore, for the asynchronous loading conditions, the Von Mises equivalent stress was calculated for the critical planes accused by MCC and MRH using the Matake criterion. It was concluded that the critical planes and their respective stresses only differ between MCC and MRH for the Matake and Susmel & Lazzarin criteria and, even for these criteria, only two synchronous loading conditions gave conflicting results. Among the asynchronous conditions, the shear stress amplitudes obtained by MRH are on average 30 MPa higher than those obtained by MCC, while the maximum normal stresses are at least 90 MPa lower. The critical orientations of the asynchronous conditions for MCC were at angle θ=90⁰, while for MRH they were at θ=45⁰ and 135⁰. For all critical planes obtained by MRH, the maximum Von Mises equivalent stress is lower than that obtained in the planes with MCC.