In this study, we investigate the possibility of applying a continuous-time ARMA (CARMA) model to radio-frequency ultrasound signals. We consider the effect of the discretization process on the parameters of the continuous system, and we take into account the exponential nature of the autocorrelation function of the model to derive continuous-domain information from the parameters of the discrete ARMA process. We validate the effectiveness of the CARMA model parameters for the characterization of ultrasound tissues on a sequence of phantom images that represent various concentrations of scatterers. We also compare the proposed CARMA coefficients and the traditional ARMA parameters on the basis of their performance in discriminating between phantom tissues. We show that working in the continuous domain brings additional useful information to characterize the imaged materials.