Two hysteresis models are investigated for modeling static hysteresis phenomenon in nonoriented magnetic steels. First, the static Preisach model is studied, and two types of experimental data, i.e., first-order reversal curves (FORCs) and concentric hysteresis loops, are employed to identify the weight function. Due to negative values in the obtained experimental weight functions, the resulting Preisach models show nonphysical behavior. To eliminate this nonphysical behavior, an optimization procedure is applied to remove these negative values. The nonphysical behavior is resolved in the modified Preisach model; however, the model still has poor accuracy for asymmetric loops. Alternatively, a new congruency-based static hysteresis model is proposed. In this model, third- or higher-order reversal curves are approximated using measured FORCs and second-order reversal curves (SORCs) by means of a congruency regularity. According to this regularity, any third- or higher-order reversal curve is congruent to SORCs with the same reversal point. A 3-D piece-wise interpolation function is employed to interpolate the measured major loop, FORCs, and SORCs. The proposed model results are compared with quasi-static measurements. The comparison reveals that the model is capable of approximating the magnetization curves for the measurements containing complex-shaped $B$ waveforms with a relative energy error of less than 4%.