Choosing two skew-cosh Gaussian beams, an analytical investigation of a medium having spherical and cylindrical core-shell nanoparticles (NPs) is performed for the generation of tunable terahertz (THz) radiation. The core of the NPs is considered to be made up of silica which is concentrically wrapped by the graphite shell. The basal planes of NPs / graphite are taken to be in parallel or perpendicular direction with the lasers electric field. In this phenomenon, the incident beams provide nonlinear velocity to the electron cloud of the NPs, leading to a nonlinear current and hence the THz emission. After obtaining an expression of nonlinear current, the THz field is calculated making use of Maxwell’s equations along with the effective permittivity governed by the radii of core and shell of the NPs. Tunable THz radiations are obtained by judiciously varying the radii of core and shell. In order to tune the focus of radiation, the resonance peaks can be made to shift towards higher frequencies, i.e., 10.4 THz and 49.4 THz, depending on the longitudinal and transverse plasmon resonances, respectively. The parameters of laser beams and NPs can be exploited for achieving efficient THz radiation.