This study was carried out to predict the time spell to first employment and to determine the effects of related factors on the timing of first employment on new graduates from Debre Markos University using survival models. The study used the 2018 Debre Markos University graduate tracer survey data. Cox PH and parametric accelerated failure time models were used. The Akaike information criterion (AIC) was used to select the best parametric model that could explain the waiting time to first employment. The median waiting time to first employment of graduates was found to be 15 months, showing that 50% of graduates managed to find their first job 15 months after their graduation date. In a comparison among parametric survival models, the log-logistic parametric model was better in describing the timing of graduates to first employment. Covariates such as gender, cumulative grade point average (CGPA) earned from the university, age at graduation, residence, field of study preference of graduates, and college/faculty were found to be statistically significant (p value <0.05) predictors of the waiting time to first employment. The log-logistic parametric model fitted the waiting time to the first employment data well and could be taken as an alternative for the Cox PH model.