Rotor vibrations and its control is an important subject in many industries such as power plants and gas stations. When lateral vibrations of rotors during operation exceed allowable level, a huge damage will be occurred. Surge and stall may be some common reasons of these vibrations. This paper aims to present a simple model for surge and stall and assumes that its effect as a distributed force acting on a rotor-disk system. This is a basic and conceptual model for future investigations in this area. Therefore, the effect of a distributed axial force exerted on an assembled disk on a rotating shaft is investigated theoretically. The set of equations for free and forced whirling analyses of a rotor- disc is derived. Also, transverse load composed of unbalanced mass and total weight of the system is considered. For forced whirling analysis, static deflection of the rotor is considered as the initial conditions and rotational speed of the rotor is considered as a time variable parameter which increases from zero to its nominal value in a limited period of time. For a simply supported rotor, the free whirling analysis is investigated using Galerkin method and using Galerkin and Newmark-beta methods, the forced whirling analysis is studied numerically. Forward and backward frequencies and Campbell diagrams are presented in free whirling analysis and variation of deflection, and shear force in any point of the rotor are depicted versus time in forced whirling analysis. The most advantages of the presented paper are consideration of time-dependency of rotating speed in forced whirling analysis. Results indicate that the axial load has a considerable effect on the forward and backward frequencies and lateral vibration amplitude of the rotor.