Resolving critical incidents can be extremely physically demanding for police officers. Consequently, throughout the selection process, training, and working career, police officers' physical abilities are often assessed with a battery of tests. Research has been conducted with a total sample of 523 students (232 female and 291 male) at the University of Criminal Investigation and Police Studies (UCIPS), with the aim of defining the norms for Linear sprint performance at 20 m (LSP20m), Illinois agility test (IAT) and Shuttle run 300-yard (ShR300y). The homogeneity of the results has been established by the low skewness and kurtosis coefficient, as well as by the values obtained from the Kolmogorov-Smirnov test, meaning the data are not significantly statistically different from the normal distribution. Based on the percentile distribution, qualitative and quantitative normative values have been defined for LSP20m, IAT and ShR300y. The achievement levels have been ranked as follows: < P10 (insufficient), P10 to P25 (poor), P25 to P50 (fair), P50 to P75 (good), P75 to P90 (very good) and > P90 (excellent). LSP20m, IAT and ShR300y tests can be used for assessing acceleration, running speed and change-of-direction speed in the anaerobic work regime. Furthermore, they correspond to the first stage of critical incidents resolution-getting to the problem (hence can be viewed as job-related fitness tests). Since population norms have been established, their implementation in the battery of tests for the assessment of UCIPS stu-dents' physical abilities in the sense of running tests can be quantitatively applied at the situational system of testing of Specialized Physical Education.