Concrete compressive strength is one of the most important concrete requirements that can be used to decide if the concrete is structurally acceptable or not. In several cases there is a need to estimate the concrete compressive strength on the site during construction or later on during the life of concrete. There are several methods used for this purpose, among the mostly used methods are the Ultra sonic pulse velocity and the Schmidt hammer rebound number. In this work six different fine aggregate and two different coarse aggregate were obtained from different parts of southern Iraq. Using these different aggregate combinations, 120 different concrete mixes with mix proportions of 1:2:4 or 1:1.5:3 and W/C ratios ranging between 0.40 to 0.60 were cast into 152 mm cubes. The compressive strength, ultrasonic pulse velocity, Schmidt hammer’s rebound number and concrete density were measured. These results were introduced into nonlinear multiple variable regressions to obtain correlation relationships to predict the concrete compressive strength. Two groups of regressions were formulated, the first used only the Ultrasonic pulse velocity and rebound number in the regressions, and separate regressions were prepared for each single source of aggregate. The results of the predicted strength was in good agreement with the experimentally measured values, the value of the standard errors of these regressions were less than 10% of the lowest concrete strength investigated (20MPa). In the second group of regressions, the data from all concrete mixes with different aggregate sources were combined together to obtain the correlation regressions. These regressions were formulated because in many cases in practice the source of aggregate may not be known exactly. Two subgroups were developed, with different independent variables combinations. The standard error of this group was higher than for the first group, its best value was 16% of the minimum value of concrete strength investigated. This clearly proves the importance of the aggregate source on the predicted concrete compressive strength values