In　this　paper,　a　peridynamic　differential　operator　(PDDO)　method　is　developed　to　analyze　the　static　and　dynamic　responses　of　size-dependent　elastic　structures　in　the　frame　of　a　consistent　couple　stress　theory　(CCST).　The　displacement　governing　equations　together　with　the　boundary　conditions　of　the　couple-stress　static　problems　are　transformed　from　the　local　differential　form　to　the　nonlocal　integral　form　through　a　fourth-order　PDDO　and　then　solved　by　a　meshfree　scheme.　For　dynamic　cases,　the　time-domain　problems　are　first　transformed　into　frequency　domain　by　Fourier　transform,　then　solved　by　the　PDDO　meshless　method　in　the　frequency　domain.　The　timedomain　results　are　finally　obtained　by　using　an　exponential　window　method　(EWM).　The　size　effects　on　the　static　and　dynamic　responses　of　some　typical　elastic　problems　are　investigated　by　the　developed　PDDO　method.　A　very　high　level　of　computational　accuracy　is　achieved　by　comparing　with　the　analytical　solutions　and　the　existing　numerical　results.