We　study　the　effect　of　softness　of　the　microchannel　on　the　process　of　droplet　generation　in　two-phase　flows　in　a　T-junction　microchannel.　One　side　of　the　microchannel　has　a　flexible　thin　PDMS　layer,　which　vibrates　naturally　while　droplets　are　generated;　the　deformation　frequency　coincides　with　the　frequency　of　droplet　formation.　Furthermore,　we　compare　the　polydispersity　of　water-in-oil　droplets　formed　with　a　microchannel　with　one　soft　wall　with　those　formed　in　a　conventional　rigid　microchannel.　We　show　that　deformation　of　the　soft　wall　reduces　the　polydispersity　in　the　droplet　size.