The present work concerns the problem of refraction artifacts in ultrasonic transmission tomography. The reconstruction is improved by curved-ray methods, combined with algebraic reconstruction techniques. The problem of acoustic ray tracing and image interpolation has been carefully studied, and different reconstruction algorithms have been developed and compared. The effect of the geometrical characteristics of the set-up and the studied medium characteristics (geometry and acoustical properties) on the reconstruction accuracy are considered. Some simulation results are presented which show an encouraging reduction of the refraction artifacts. The results have been confirmed by experiments carried out with agar-gel phantoms. The experimental device and procedure are described and straight- and curved-ray reconstructions are shown. Reconstruction quality can be improved significantly for refractive index variations of up to 10%, which seems sufficient for soft tissue imaging; yet there are some limiting factors, such as multipath propagation, if any, or the difficulty of choosing an initial value for the reconstruction.