Capillary dynamics is a ubiquitous everyday phenomenon. It has practical applications in diverse fields, including ink-jet printing, lab-on-a-chip, biotechnology, and coating. Understanding capillary dynamics requires essential knowledge on the molecular level of how fluid molecules interact with a solid substrate (the wall). Recent studies conducted with the surface force apparatus (SFA), atomic force microscope (AFM), and statistical mechanics simulation revealed that molecules/nanoparticles confined into the film/wall surfaces tend to self-layer into 2D layer/s and even 2D in-layer with increased confinement and fluid volume fraction. Here, the capillary rise dynamics of simple molecular fluids in cylindrical capillary is explained by the molecular self-layering model. The proposed model considers the role of the molecular shape on self-layering and its effect on the molecularly thin film viscosity in regards to the advancing (dynamic) contact angle. The model was tested to explain the capillary rise dynamics of fluids of spherical, cylindrical, and disk shape molecules in borosilicate glass capillaries. The good agreement between the capillary rise data and SFA data from the literature for simple fluid self-layering shows the validity of the present model. The present model provides new insights into the design of many applications where dynamic wetting is important because it reveals the significant impact of molecular self-layering close to the wall on dynamic wetting.