Reliability prediction of highly safe mechanical systems can be performed using classical tail modeling. Classical tail modeling is based on performing a relatively small number of limit-state evaluations through a sampling scheme and then fitting a tail model to the tail part of the data. However, the limit-state calculations that do not belong to the tail part are discarded, so majority of limit-state evaluations are wasted. Guided tail modeling, proposed earlier by the author, can provide a remedy through guidance of the limit-state function calculations toward the tail region. In the original guided tail modeling, the guidance is achieved through a procedure based on threshold estimation using univariate dimension reduction and extended generalized lambda distribution and tail region approximation using univariate dimension reduction. This article proposes a new guided tail modeling technique that utilizes support vector machines. In the proposed method, named guided tail modeling with support vector machines (GTM-SVM), the threshold estimation is still performed using univariate dimension reduction and extended generalized lambda distribution, while the tail region approximation is based on support vector machines. The performance of guided tail modeling with support vector machines is tested with mathematical example problems as well as structural mechanics problems with varying number of variables. GTM-SVM is found to be more accurate than both guided tail modeling and classical tail modeling for low-dimensional problems. For high-dimensional problems, on the other hand, the original guided tail modeling is found to be more accurate than guided tail modeling with support vector machines, which is superior to classical tail modeling.