A main limitation of most models describing the effect of stress on the magnetic behavior is that they are restricted to uniaxial, tensile or compressive, stress. An idea to overcome this strong limitation is to define a fictive uniaxial stress, the equivalent stress that would affect the magnetic behavior in a similar manner than a multiaxial one. Several authors have tried to define such a criterion. We propose in this paper to compare several equivalent stress definitions, and to apply them in the case of uniaxial and biaxial mechanical loadings for which experimental results are available.