The growth of a cylindrical spark discharge channel in water and Lexan is studied using a series of one-dimensional simulations with the finite-element radiation-magnetohydrodynamics code ALEGRA. Computed solutions are analyzed in order to characterize the rate of growth and dynamics of the spark channels during the rising-current phase of the drive pulse. The current ramp rate is varied between 0.2 and 3.0 kA/ns, and values of the mechanical coupling coefficient Kp are extracted for each case. The simulations predict spark channel expansion velocities primarily in the range of 2000 to 3500 m/s, channel pressures primarily in the range 10-40 GPa, and Kp values primarily between 1.1 and 1.4. When Lexan is preheated, slightly larger expansion velocities and smaller Kp values are predicted, but the overall behavior is unchanged.