We report on sub-30 fs pulse generation from a semiconductor saturable absorber mirror mode-locked Yb:YAP laser. Pumping by a spatially single-mode Yb fiber laser at 979 nm, soliton pulses as short as 29 fs were generated at 1091 nm with an average output power of 156 mW and a pulse repetition rate of 85.1 MHz. The maximum output power of the mode-locked Yb:YAP laser amounted to 320 mW for slightly longer pulses (32 fs) at an incident pump power of 1.52 W, corresponding to a peak power of 103 kW and an optical efficiency of 20.5%. To the best of our knowledge, this result represents the shortest pulses ever achieved from any solid-state Yb laser mode-locked by a slow, i.e., physical saturable absorber.