Accurate hysteresis models are necessary for modeling of magnetic components of devices such as transformers and motors. This study presents a hysteresis model with a convenient analytical form, based on hypergeometric functions with one free parameter, built upon a class of parameterized curves. The aim of this work is to explore suitability of the presented model for describing major and minor loops, as well as to demonstrate improved agreement between experimental and modeled hysteresis loops. The procedure for generating first order reversal curves is also discussed. The added parameter, introduced into the model, controls the shape of the model curve, especially near saturation. It can be adjusted to provide better agreement between measured and model curves. The model parameters are nonlinearly dependent; therefore, they are determined in a nonlinear curve fitting procedure. The choice of the initial approximation and a suitable set of constraints for the optimization procedure are discussed. The inverse of the model function, required to generate first order reversal curves, cannot be obtained in analytical form. The procedure to calculate the inverse numerically is presented. Performance of the model is demonstrated and verified on experimental data obtained from measurements on construction steel sheets and grain-oriented electrical steel samples.