In industrial equipment containing hydraulic lines for power transmission, the lines have boundary conditions defined by components such as pumps, valves, and actuators located at the ends of the lines. Sudden changes in any of the boundary conditions may result in significant pressure/flow dynamics (fluid transients) in the lines that may be detrimental or favorable to the performance of the equipment. Accurate models for line transients are defined by a set of simultaneous partial differential equations. In this paper, analytical solutions to the partial differential equations provide Laplace transform transfer functions applicable to any set of boundary conditions yet to be specified that satisfy the requirements of causality. Analytical solutions from previous publications are reviewed for cases of laminar and turbulent flow for Newtonian and a class of non-Newtonian fluids. When obtaining time domain simulations for specific boundary conditions, complexities associated with the inverse Laplace transform are avoided by using an inverse frequency algorithm. Examples with pumps, valves, and actuators demonstrate the process of coupling equations for components at the ends of a line to get total system transfer functions and then obtaining time domain solutions for outputs-of-interest associated with system inputs and load variations.