The increasing coupling between natural gas and electricity systems by gas-fired generation units brings new challenges to system analysis, such as pressure variations due to consumption perturbations of generation units. The emerging issues require revolutionary modeling and analysis techniques. This paper proposes a novel model to quantify gas pressure variations due to gas-fired power unit ramping and the impact of constraints from natural gas pressure change on ramp rates of gas-fired plants. By utilizing Laplace transform to resolve the governing equations of gas networks, the proposed model can significantly reduce modeling complexity and computational burden. The dynamic behaviors in time scale in s-domain and spatial partial differential equations are transformed into finite difference equations. By introducing the concept of transfer matrices, the relation between states at each node of gas systems can be expressed by transfer parameter matrices. Additionally, a simplified model is introduced to simply the analysis. The explicit expressions of nodal pressure variations in response to demand change are very convenient for analyzing system dynamic performance under disturbances, identifying the most influential factors. The new models are extensively demonstrated on three natural gas networks and benchmarked with traditional simulation approaches. Results illustrate that they produce very close results with the simulation approach, particularly when gas pipelines are long and enter steady states.