Dynamic properties of printed circuit board (PCB) assembly under drop impact are investigated when viscoelasticity of substrate materials is considered. The main materials of a PCB substrate are macromolecule resins, which are typical viscoelastic materials. From the viewpoint of viscoelasticity, the dynamics of PCBs under drop impact is analyzed based on mass-damping-spring, beam, and plate theories. It is demonstrated that the viscoelasticity of a PCB has distinct influences on the dynamic properties of PCBs under board-level drop impact. When there is an increase in the viscosity of substrate materials, the damping coefficients of PCBs would rise, its deflection and acceleration responses could diminish faster, and the maximum deflection of PCBs would become smaller. Meanwhile, with the same viscosity and drop impact conditions, a larger plate would produce a bigger deflection response. Therefore, drop impact reliability could be enhanced by choosing substrate material of larger viscoelasticity and reducing properly the size of PCBs. Dynamic analysis of PCBs under drop impact not only contributes to perfecting theoretical research, but also provides a reference for the choice of substrate materials and reliability design of PCBs when electronic products are devised.