Pose estimation from points with unknown correspondences currently is still a difficult problem in the field of computer vision. To solve this problem, the SoftSI algorithm is proposed, which can simultaneously obtain pose and correspondences. The SoftSI algorithm is based on the combination of the proposed PnP algorithm (the SI algorithm) and two singular value decomposition (SVD)-based shape description theorems. Other main contributions of this paper are: 1) two SVD-based shape description theorems are proposed; 2) by analyzing the calculation process of the SI algorithm, the method to avoid pose ambiguity is proposed; and 3) an acceleration method to quickly eliminate bad initial values for the SoftSI algorithm is proposed. The simulation results show that the SI algorithm is accurate while the SoftSI algorithm is fast, robust to noise, and has large convergence radius.