It is well known that the mechanical strength of iron is significantly changed by alloying. However, atomistic origin and underlying mechanism are still unclear. Since the strength change with respect to solute concentration is very sensitive and highly non-linear, the way of empirical prediction may contribute little to designing the mechanical strength by alloying. In this study, we theoretically construct a model which predicts temperature, strain rate, and solute concentration dependencies on critical resolved shear stress (CRSS) and yield stress of BCC iron alloys with dilute substitutional solutes based on atomistic analysis of the dislocation-solute atom interaction. In the coarse-grained BCC polycrystalline metals, the mechanical strength and deformation are dominated by screw dislocation motion consisting of kink nucleation and migration processes. Thus, our model is based on atomistically computed activation free energies for kink nucleation and migration of screw dislocation. We eventually apply our model to Fe-Si dilute alloy system as a representative example of BCC dilute alloys, and the theoretically predicted CRSS by our model is compared with an experimental one.