During delivery, quantitative information on the uterine activity can be provided by internal uterine pressure (IUP) recordings using an invasive intrauterine pressure catheter (IUPC). The electrohysterogram, which measures the electrical signal that drives the mechanical contraction of the uterine muscle and the consequent IUP increase, is recorded by electrodes placed on the abdomen. Recent work demonstrated the possibility of reliably estimating the IUP noninvasively by electrohysterographic (EHG) signal analysis. To further improve the accuracy of IUP estimates, we investigated the use of three nonlinear functions for modeling the relationship between the electrical activation measured by the EHG signal and the mechanical response of the uterine muscle. The feature employed for obtaining a first estimate of the IUP is the unnormalized first statistical moment of the EHG spectrum. The relationship between the extracted feature and the IUP is modeled by a second-order polynomial, a logarithmic, and an exponential function. For validation, the IUPC and the EHG signals were recorded on nine women in labor. A second-order polynomial model already provided estimates that are highly correlated with the IUPC signal (r = 0.73). However, the logarithmic model resulted to be the most accurate, especially in terms of root mean squared error (RMSE = 5.13 mmHg).