Spanner construction is one of the most important techniques for topology control in wireless networks. A spanner can help not only to decrease the number of links and to maintain connectivity but also to ensure that the distance between any pair of communication nodes is within some constant factor from the shortest possible distance. Due to the non-locality, constructing a spanner is especially challenging under the physical interference model signal-to-interference-and-noise-ratio (SINR). In this paper, we develop two localized randomized algorithms SINR-directed-YG and SINR-undirected-YG to construct a directed Yao graph (YG) and an undirected YG in O(log n) (n is the number of wireless nodes) time slots with a high probability, in which each node is capable of performing successful local broadcasts to gather neighborhood information within a certain region and the SINR constraint is satisfied at all the steps of the algorithms. The resultant graph of SINR-undirected-YG, which is based on SINR-directed-YG, possesses a constant stretch factor 1/1-2 sin(π/c), where c > 6 is a constant. To the best of our knowledge, SINR-undirected-YG is the first spanner construction algorithm under SINR. We also obtain Yao-Yao graph under SINR. Extensive theoretical performance analysis and simulation study are carried out to verify the effectiveness and the efficiency of our proposed algorithms.