AbstractThe stationary universe solutions have been studied using the metrics of VAN Stockum(1937) and Gödel(1949) in a New ST theory (Saezand Ballester, 1985), general relativity with variable cosmological term (Narlikaret al., 1991), Lyra's geometry (Sen, 1957) and Cosmic strings. It has been shown that the stationary universe has rigid rotation in ST theory. In the presence of variable cosmological term, there is non‐rigid rotation in the presence of Zeldovich fluid for van Stockum metric. In Lyra's geometry the only solution is possible when the gauge function β is variable and there is Zeldovich fluid. However, in the presence of cosmic strings, there is no solution with van Stockum or Gödel met