We demonstrated that sound can push fluid through a tissue-mimicking material. Although acoustic streaming in tissue has been proposed as a mechanism for biomedical ultrasound applications, such as neuromodulation and enhanced drug penetration, streaming in tissue or acoustic phantoms has not been directly observed. We developed a material that mimics the porous structure of tissue and used a dye and a video camera to track fluid movement. When applied above an acoustic intensity threshold, a continuous focused ultrasound beam (spatial peak time average intensity: 238 W/cm2, centre frequency: 5 MHz) was found to push the dye axially, that is, in the direction of wave propagation and in the radial direction. Dye clearance increased with ultrasound intensity and was modelled using an adapted version of Eckart's acoustic streaming velocity equation. No microstructural changes were observed in the sonicated region when assessed using scanning electron microscopy. Our study indicates that acoustic streaming can occur in soft porous materials and provides a mechanistic basis for future use of streaming for therapeutic or diagnostic purposes.