In contrast to X-rays, ultrasound propagates along a curved path due to spatial variations in the refraction index of the medium. Thus, for ultrasonic TOF tomography, the propagation path of the ultrasound must be known to correctly reconstruct the slice image. In this paper, we propose a new path determination algorithm, which is essentially a numerical solution of the eikonal equation viewed as a boundary value problem. Due to the curved propagation path of ultrasound, the image reconstruction algorithm takes the algebraic approach, for instance, the ART or the SART. Note that the image reconstruction step requires the propagation path and the paths can be determined only if the image is known. Thus, an iterative approach is taken to solve this apparent dilemma. First, the slice image is initially reconstructed assuming straight propagation paths. Then the paths are computed based on the recently reconstructed image using our path determination algorithm and used to update the reconstructed image. The process of the image reconstruction and the path determination repeats until convergence. This is the approach taken in this paper and it is tested using both a simulation data and a real concrete structure scanned by a mechanical scanner.