In this paper, the aerodynamic and aeroelastic effects of part-span shrouds are both investigated by means of numerical simulations. Based on a well-publicized NASA Rotor 67, a modified transonic fan rotor with the inclusion of a fictitious but typical part-span shroud, is selected to be studied. First, by CFD technique, three-dimensional steady-state calculations are performed for aerodynamic study. Numerical results show that the flow blockage and associated flow losses are caused and would become more severe as the operating condition approaches to the stall margin. It is also found that the presence of part-span shrouds could delay the occurrence of stall and extends the operating range. Further, the pressure distributions at different sections of the unshrouded and shrouded blades are compared and relevant analysis is presented. On the other hand, for aeroelastic study, by directly coupling CFD and CSD computations in the time domain, an effective fluid-structure coupled system is constructed. Considering the speciality of the shrouded blade, some special issues on both aerodynamic and structural modeling are discussed. Particularly, respectively corresponding to situations of in-phase and anti-phase vibrations, a single passage model and a double passage model are used. Comparative study shows that the presence of part span shrouds greatly improves the convergence rates of all modes, numerically verifying their positive effects on aeroelastic stability. Also it is shown that the blade vibrating in opposite phase has a better aeroelastic stability. Besides, since the aeroelastic effect of part-span shrouds is a combined result of aerodynamic and structural factors, this paper also solely assesses the influence of aerodynamic factor by ignoring the forces on the contact plane. The numerical results show that its effect may be negative but negligibly small.