Plastic deformation of granular layers in railway tracks under cyclic loading is a key factor controlling the substructure’s stability. In particular, the granular subballast capping layer placed between the ballast and subgrade can undergo permanent deformations due to the moving wheel load of trains. This study was conducted to evaluate the cyclic behavior of recovered plastic (RP) blended at different percentages with construction and demolition (C&D) aggregates as railway subballast capping layer. Recycled concrete aggregate (RCA) and crushed brick (CB) were used as the parent C&D aggregates. Multistage triaxial compression tests were initially undertaken to determine the shear strength and the effect of RP inclusion on strength characteristics. The results of multistage triaxial compression tests were also used to find a link between static shear strength and cyclic deformation of the granular recycled materials. The plastic deformability of the RP + C&D blends was also assessed through multistage cyclic triaxial tests at three confining pressures and incremental deviator stress at each confinement. The shakedown theory was employed to characterize the changes in permanent axial and radial deformations, resilient axial strain, and permanent axial strain rate. Inclusion of RP in the RP + C&D blends was found to increase the sample’s deformability particularly in the secondary phase of deformation, reduced the stiffness, and most importantly increased the rate of permanent strain accumulation.