The internal ballistic analysis of a solid rocket motor mainly relies on an accurate computation of the transient burning surface geometry of the propellant during combustion phase. A reliable and an efficient burnback analysis is crucial in order to predict the ballistic performance of a solid rocket motor in early design processes. Because analytical burnback solutions provide exact results in the most affordable time, derivation of analytical solutions for generic propellant geometries is of practical value and high importance for rocket designers. This paper summarizes a research effort for developing a computational tool based on burnback analytics for all possible different geometric configurations of a generic slotted-type propellant. After the burnback solutions were verified and implemented into an in-house code, this parametric and analytical tool is integrated into a zero-dimensional internal ballistic solver to enable an efficient overall computational framework to be employed for multidisciplinary design and optimization of solid rocket motors.