A one-dimensional, quasistatic model of a capillary discharge plasma has been developed. Such a plasma is useful as a medium to generate plasma waves for acceleration of electrons via processes such as laser wakefield acceleration or plasma wakefield acceleration. Another important characteristic of the plasma is its intrinsic parabolic density distribution near the center of the capillary, which can channel a laser beam along the capillary. The model is intended to be a design tool to aid in the selection of the capillary parameters in order to obtain desired plasma characteristics, e.g., plasma density and matched laser beam radius for guiding. An optional external axial magnetic field can be included, which improves the laser-channeling effect in some cases. The model also enables a measure of the potential for laser damage of the capillary wall. Results are presented for the design of a gas-filled capillary that will be tested during the staged electron laser acceleration -laser wakefield (STELLA-LW) experiment.