We propose a calibration-free photoacoustic (PA) method for transverse flow measurements. In this method, a pulsed periodically structured (i.e., grating patterned) optical beam is used to illuminate flowing absorptive particles in an optically scattering medium. The PA signal amplitudes measured over consecutive laser pulses carry an imprint of the illumination structure. The modulation frequency of the imprint is proportional to the component of the flow speed projected onto the normal axis of the striped illumination pattern. This method can tolerate high particle density, and is insensitive to the particle size, thus calibration-free. Bovine blood and microsphere phantoms were used to validate the proposed method. Blood flow in a mouse ear was measured in vivo as well.