The nonintuitive observation of the simultaneous high velocity and high attenuation of ultrasonic waves near the freezing point of brine was previously measured in partially frozen systems. However, previous studies could not fully elucidate the attenuation variation of ultrasonic wave propagation in a partially frozen system. We have investigated the potential attenuation mechanisms responsible for previously obtained laboratory results by modeling ultrasonic wave transmission in two different partially frozen systems: partially frozen brine (two phases composed of ice and unfrozen brine) and unconsolidated sand (three phases composed of ice, unfrozen brine, and sand). We adopted two different rock-physics models: an effective medium model for partially frozen brine and a three-phase extension of the Biot model for partially frozen unconsolidated sand. For partially frozen brine, our rock-physics study indicated that squirt flow caused by unfrozen brine inclusions in porous ice could be responsible for high P-wave attenuation around the freezing point. Decreasing P-wave attenuation below the freezing point can be explained by the gradual decrease of squirt flow due to the gradual depletion of unfrozen brine. For partially frozen unconsolidated sand, our rock-physics study implied that squirt flow between ice grains is a dominant factor for P-wave attenuation around the freezing point. With decreasing temperature lower than the freezing point, the friction between ice and sand grains becomes more dominant for P-wave attenuation because the decreasing amount of unfrozen brine reduces squirt flow between ice grains, whereas the generation of ice increases the friction. The increasing friction between ice and sand grains caused by ice formation is possibly responsible for increasing the S-wave attenuation at decreasing temperatures. Then, further generation of ice with further cooling reduces the elastic contrast between ice and sand grains, hindering their relative motion; thus, reducing the P- and S-wave attenuation.