We consider the following basic link capacity (a.k.a., one-shot scheduling) problem in wireless networks: Given a set of communication links, find a maximum subset of links that can successfully transmit simultaneously. Good performance guarantees are known only for deterministic models, such as the physical model with geometric (log-distance) pathloss. We treat this problem under stochastic shadowing under general distributions, bound the effects of shadowing on optimal capacity, and derive constant approximation algorithms. We also consider temporal fading under Rayleigh distribution, and show that it affects non-fading solutions only by a constant-factor. These can be combined into a constant approximation link capacity algorithm under both time-invariant shadowing and temporal fading.