Compressive strength and ultrasonic pulse velocity (UPV) are two of the most preferred technics for determining both mechanical properties and microstructural characteristics of cement-based materials. Since the most important mechanical property of concrete compared to many other properties is its compressive strength, it is of great importance to predict and determine the compressive strength. In the current investigation, the compressive strength and ultrasonic pulse velocities of twelve (12) different cement mortars containing different amounts of fly ash and nano calcite were experimentally obtained for the curing ages of 1, 3, 7, 28 and 90 days. By using the experimentally obtained data, compressive strength was estimated by the regression methods developed using the extreme learning machine (ELM), support vector machine (SVM) and group method of data handling (GMDH). In order to compare both experimental and predicted results and also to measure their performance, coefficient of determination (R-2) and mean squared error (MSE) were utilized. Two different methods were made for each regression method. These were; Method 1: Estimation of compressive strength values without including UPV test results and Method 2: Estimation of compressive strength values including UPV results. Thus, the relationship between (i) the compressive strength and UPV experimental results and (ii) the estimation results of the regression models were determined and then compared. In this study, the best test performances (namely, for R-2/MSE) were found as 0.917/20.239 with the ELM model in the Method 1; 0.982/3.882 with the SVM model in the Method 2. According to these results, it was revealed that the selected regression models achieved high success in the estimation of compressive strength.