Despite its known effectiveness, a typical vibratory assembly method tends to generate adverse impact forces between mating parts commensurate with the relatively large vibratory motion required for reliably compensating positioning errors of arbitrary magnitude. To this end, this paper presents a neural network-based vibratory assembly method with its emphasis on reducing the mating forces for chamferless prismatic parts. In this method, the interactive force is effectively suppressed by reducing the amplitude of vibratory motion, while the greater part of the relative positioning error is estimated and compensated by a neural network. The estimation performance of the neural network and the overall performance of the assembly method are evaluated experimentally. Experimental results show that the assembly is efficiently accomplished with small reaction forces, and the possible insertion error range is also expanded