This paper addresses implementations of tangent hyperbolic and sigmoid functions using stochastic logic. Stochastic computing requires simple logic gates and is inherently fault-tolerant. Thus, these structures are well suited for nanoscale CMOS technologies. Tangent hyperbolic and sigmoid functions are widely used in machine learning systems such as neural networks. This paper makes two major contributions. First, two approaches are proposed to implementing tangent hyperbolic and sigmoid functions in unipolar stochastic logic. The first approach is based on a JK flip-flop. In the second approach, the proposed designs are based on a general unipolar division. Second, we present two approaches to computing tangent hyperbolic and sigmoid functions in bipolar stochastic logic. The first approach involves format conversion from bipolar format to unipolar format. The second approach uses a general bipolar stochastic divider. Simulation and synthesis results are presented for proposed designs.