The analytical study described in this report examines changes in the useful frequency response of short pressure probes resulting from variations in the viscous damping within the probe tube. The study is based on the use of the Bergh and Tijdeman recursion formula, which was modified to allow the addition of arbitrary amounts of viscous loss in any tube section. Results show that the useful response range can be increased with damping but is dependent on the operating temperature and pressure levels. At 300 K, only a 15-percent variation in average pressure is allowable if the useful response is to be a factor of three higher than that of an undamped probe. This variation increases to 20 or 30 percent at temperatures above 600 K. A computer program based on the modified recursion formula is given in an appendix.