In this work, deep neural networks (DNNs) are trained and used to model high-speed channels for signal integrity analysis. The DNN models predict eye-diagram metrics by taking advantage of the large amount of simulation results made available in a previous design or at an earlier design stage. The proposed DNN models characterize high-speed channels through extrapolation with saved coefficients, which requires no complex simulations and can be achieved in a highly efficient manner. It is demonstrated through numerical examples that the proposed DNN models achieve good accuracy in predicting eye-diagram metrics from input design parameters. In the DNN models, no assumptions are made on the distributions of and the interactions among individual design parameters.