A method for the sparse solution of ε-tube support vector regression machines is presented. The proposed method achieves a high accuracy versus complexity ratio and allows the user to adjust the complexity of the resulting models. The sparse representation is guaranteed by limiting the number of training data points for the support vector regression method. Each training data point is selected based on its influence on the accuracy of the model using the active learning principle. The training time can be adjusted by the user by selecting how often the hyper-parameters of the algorithm are optimised. The advantages of the proposed method are illustrated on several examples. The algorithm performance is compared with the performance of several state-ofthe-art algorithms on the well-known benchmark data sets. The application of the proposed algorithm for the black-box modelling of the electronic circuits is also demonstrated. The experiments clearly show that it is possible to reduce the number of support vectors and significantly improve the accuracy versus complexity ratio of ε-tube support vector regression.