Abstract: Cutter wear and frequent cutter change in hard rock tunneling are the main factors limiting an efficient tunneling. Low-pressure abrasive air jet assisted cutter rock breaking is a feasible idea to break through the bottleneck of rock breaking technology in hard rock tunnel. To achieve assisted high traverse speed cutter breaking, a rectangular nozzle was proposed. The rectangular nozzle can effectively improve the agglomeration of the abrasive in the moving direction, thereby reducing the cutting width, and improve the cutting depth. To clarify the influence of rectangular nozzle on abrasive acceleration and rock breaking, a circular nozzle and a rectangular nozzle were designed with approximately equivalent lengthening divergent section length and cross-section, and then the influence of nozzle divergent section length on gas and abrasive acceleration was determined based on numerical methods, and the influence of different cross-sectional shapes of nozzles on abrasive acceleration and distribution characteristics were comparatively analyzed. Finally, by carrying out the low-pressure abrasive air jet erosion crushing granite experiment, the influence of nozzle structure and traverse velocity on the erosion effect was studied, the cutting efficiency of nozzles with different cross-sectional shapes was analyzed, and the optimal nozzle structure suitable for rock breaking by assisted tools was determined. The numerical study results show that when the pressure is 2 MPa, the length of the divergent section is extended, the gas-solid two-phase energy conversion is more complete, and the abrasive acceleration is more sufficient, but with the continuous lengthening of the nozzle divergent section, the abrasive speed is not significantly increased. Compared with the circular nozzle, the rectangular nozzle is slightly worse at the abrasive acceleration, but it can still accelerate the abrasive to 300 m/s, and the abrasives accelerated by the rectangular nozzle are distributed flat and rectangular in the free flow basin, which effectively improves the agglomeration of the abrasive in the horizontal movement direction of the cutter. Experiments show that the divergent section of the circular nozzle is lengthened, and the erosion depth of rock is increasing, when the length of the divergent section is 145 mm, the erosion depth of granite is 23.90 mm and 20.23 mm, respectively, and the continuous lengthening of the divergent section length, and the erosion depth of rock is not significantly improved. When the traverse speed is 0.02 m/s, the cutting depths of basalt of nozzles C₄, R₁ and R₂ are 3.35 mm, 12.15 mm and 8.25 mm, and the granite depths are 5.2, 14.9 and 11.5 mm, respectively. When the traverse speed is 0.30 m/s, the depths of basalt cutting by nozzles C₄ and R₁ are 0.8 mm and 3.0 mm, and the granite depths are 1.0 mm and 3.6 mm, respectively. Compared with the nozzle C₄, the same as the numerical simulation results, the rectangular nozzle can make the abrasive energy concentrate, the abrasive utilization is fully utilized, and the cutting efficiency is better. And the cutting efficiency of nozzle R₁ is the best, and the nozzle structure is the best. The research will provide theoretical and technical support for the abrasive air jet assisted cutter rock breaking.