We provide computationally generated dataset simulating propagation of ultrasonic waves in viscous tissues in two and three dimensional domains. The dataset contains physical parameters of a human breast with a high-contrast inclusion, the acquisition setup with positions of sources and receivers, and the associated pressure-wave data at ultrasonic frequencies. We simulated the wave propagation based on seven different viscous models using the physical parameters of the breast. Furthermore, different choices of conditions for the medium's boundaries are given, namely absorbing and reflecting boundaries. The dataset allows to evaluate the performance of reconstruction methods for ultrasound imaging under attenuation model uncertainty, that is, when the precise attenuation law that characterizes the medium is unknown. In addition, the dataset enables to evaluate the robustness of inverse scheme in the context of reflecting boundary conditions where multiple reflections illuminate the sample, and/or the performance of data-processing to suppress these multiple reflections.