Acoustic Airy beams as non-diffractive beams possess virtues of self-bending, self-healing, and non-diffraction, and are expected to have great potentials in applications like ultrasonic imaging. Here an analytical theory is provided for gaussian modulated Airy (gAiry) acoustic beams. Through numerical calculations and finite element simulations, it is revealed that gAiry beams inherit the above-mentioned merits of standard Airy beams. In theoretically predicted and more practical cases where beams are generated by sources of limited apertures, reduction of side lobes are found in gAiry fields, while bilateral focusing using a pair of beams show improved field features when compared with focused Airy fields. The theories and observations here can be helpful for deploying gAiry beams in applications.