This thesis focuses on the modeling and solutions of the simultaneous switching noise (SSN) problems in the power delivery networks (PDN) of high-speed digital circuit packages. An efficient numerical approach based on two-dimension (2D) finite-difference time-domain (FDTD) method combined with the lumped circuit model of the interconnection is proposed to model the PDN of a package and PCB. Based on this approach, the mechanism of noise coupling between package and PCB can be analyzed. In addition, a novel photonic crystal power layer (PCPL) design for the PDN of the package or PCB is proposed to suppress the SSN. The periodic High-Dk material is embedded into the substrate layer between the power and ground planes. Both modeling and measurement demonstrate the PCPL can form a wide stopband well with excellent suppression of the SSN propagation in the substrate and the corresponding electromagnetic interference (EMI).