CubeSats and other small satellites experience harsh dynamic conditions during launch, where broadband random vibration and high-frequency shock events can pose a significant risk to structural integrity and onboard components. This paper investigates the dynamic response of a CubeSat primary structure when subjected to representative launch vibration and shock environments. A finite element model of the CubeSat is developed, accounting for realistic mass distribution, structural connections, and boundary conditions imposed by the deployer interface. Modal analysis is performed to determine the fundamental natural frequencies and dominant mode shapes, enabling an assessment of compliance with commonly imposed launcher stiffness constraints. The structural response to launch-induced random vibration is then evaluated using representative power spectral density inputs, with emphasis on root-mean-square acceleration and stress levels throughout the structure. Furthermore, shock response spectrum analysis is carried out to estimate peak accelerations transmitted to critical subsystems and sensitive components. The results identify key dynamic amplification effects linked to structural layout and mass placement, as well as regions most vulnerable to launch loading. Based on these findings, design considerations and potential mitigation strategies are discussed to improve structural robustness and reduce dynamic sensitivity. The presented approach provides a practical framework for early-phase structural verification and qualification of CubeSat platforms and is applicable to a broad range of small satellite missions and launch scenarios.