Off-axis high power diode laser (HPDL) cladding is commonly used for surface quality enhancement such as coating, part repairing, etc. Although some laser cladding models are available in literature, little has been reported on the modeling of powder flow and molten pool for a rectangular beam with side powder injection. In this article, a custom-designed flat nozzle delivers the powder material into a distinct molten pool formed by a HPDL with a rectangular beam. A powder model is first presented to reveal the powder flow behavior below the flat nozzle. Key parameters such as nozzle inclination angle, rectangular beam profile, shielding gas flow rates, and powder feed rate are incorporated so that spatial powder density, powder velocity, and temperature distribution are distinctly investigated. Then in order to describe thermal and fluidic behaviors around the molten pool formed by the rectangular beam, a three-dimensional self-consistent cladding model is developed with the incorporation of the distributed powder properties as input. The level set method is adopted to track the complex free surface evolution. Temperature fields and fluid motion in the molten pool area resulting from the profile of rectangular beam are distinctly revealed. The effect of continuous mass addition is also embedded into the governing equations, making the model more accurate. A HPDL cladding with little dilution is formed and the simulated results agree well with the experiment.