A rapid nonlinear aeroelastic framework for the analysis of the highly flexible wing with distributed propellers is presented, validated and applied to investigate the propeller effects on the wing dynamic response and aeroelastic stability. In the framework, nonlinear beam elements based on the co-rotational method are applied for the large-deformation wing structure, and an efficient cylinder coordinate generation method is proposed for attached propellers at different position. By taking advantage of the relatively slow dynamics of the high-aspect-ratio wing, propeller wake is modeled as a quasi-steady skewed vortex cylinder with no updating process to reduce the high computational cost. Axial and tangential induced velocities are derived and included in the unsteady vortex lattice method. For the numerical cases explored, results indicate that large deformation causes thrust to produce wing negative torsion which limits the displacement oscillation, and slipstream mainly increases the response values. In addition, an improvement of flutter boundary is found with the increase of propeller thrust while slipstream brings a destabilising effect as a result of the increment of dynamic pressure and local lift. The great potential of distributed propellers in gust alleviation and flutter suppression of such aircraft is pointed out and the method as well as conclusions in this paper can provide further guidance.