The neutron flux-to-pressure frequency response for a molten-salt-fueled reactor with a small amount of gas entrained in the molten salt was determined analytically. The one-dimensional conservation equations describing the flow of the compressible molten-salt gas mixture and the one-group neutron diffusion equations were written in the linearized perturbed form, and Laplace transformation in time was performed. The coupled set of equations describing the conservation of mass for the molten salt, conservation of mass for the gas, and conservation of momentum for the salt-gas mixture (the hydraulic equations) was solved by employing matrix exponential techniques. The remaining equations were solved by more conventional schemes. The matrix exponential technique was selected to obtain a solution for the hydraulic equations over the techniques normally employed (nodal or modal) for stability studies in boiling water systems because the validity of the solution is independent of the frequency of interest, and the total number of simultaneous equations required to be solved for application of boundary conditions (closing the flow loop) is small. Results from the computed neutron flux-to-pressure frequency response for the molten-salt-fueled reactor under study show that the shape of the modulus of the frequency response for frequencies below 1 to 2 cycles/sec is independent of the void fraction (volume fraction occupied by the gas), and the magnitude of the modulus of the frequency response is proportional to the void fraction. Therefore, we conclude that the amount of void in the system can be inferred by comparing the analytical frequency response with an experimental frequency response. (This conclusion was verified and is reported in the following paper.)