Control of macrosegregation phenomena and deformation related defects is the main issue in solidification processes. Numerical modeling of casting provides an answer to industrial needs to master these defects. As a first step, it is essential to achieve a concurrent computation of the fluid flow in the bulk liquid and stress-strain evolution in the already solidified regions. For this specific purpose, a partitioned solution algorithm is developed to model both ingot casting and continuous casting processes: liquid flow induced by natural convection or filling step, solidification shrinkage as well as thermal deformation of solid phase are all taken into consideration. This article is mainly composed of two parts. In the first part, details of the model itself are described. In the second part, applications dedicated to steel solidification are proposed.