A parallel camera array resembles a large class of biological visual systems. It consists of two cameras moving in tandem, which have parallel viewing directions and no overlap in the visual fields. Without correspondences, we leverage on pair of parallel visual rays to remove rotational flows and obtain a quasi-parallax motion field, which leads to an accurate and parsimonious solution for translation recovery. The rotation is subsequently recovered using the epipolar constraints and benefits greatly from the good translation estimate. Experimental results show that the linear and the bundle adjustment methods achieve comparable performances.