This paper presents novel architectures for radial basis function (RBF) kernel computation for support vector machine (SVM) classifier using stochastic logic. Stochastic computing systems involve low hardware complexity and are inherently faulttolerant. Two types of architectures are presented. These include: an implementation with input and output both in bipolar format and an implementation with bipolar input and unipolar output. The computation of RBF kernel is comprised of the squared Euclidean distance and the exponential function. In the first implementation, two components are implemented in bipolar format and the exponential function is designed based on the finite state machine (FSM) method. The second implementation computes the squared Euclidean distance with bipolar input and unipolar output. The exponential function is implemented in unipolar format based on the Maclaurin expansion. The accuracies of two architectures are compared using support vectors from classification of electroencephalogram (EEG) signals for seizure prediction. From simulation results, it is shown that the computational error of the second stochastic implementation with format conversion is 24.90% less than that of the first implementation in bipolar format.