Atomically detailed distributions of ions around an A-form RNA are computed. Different mixtures of monovalent and divalent ions are considered explicitly. Studies of tightly bound and of diffusive (but bound) ions around 25 base pairs RNA are conducted in explicit solvent. Replica exchange simulations provide detailed equilibrium distributions with moderate computing resources (20 ns of simulation using 64 replicas). The simulations show distinct behavior of single and double charged cations. Binding of Mg(2+) ion includes tight binding to specific sites while Na(+) binds only diffusively. The tight binding of Mg(2+) is with a solvation shell while Na(+) can bind directly to RNA. Negative mobile ions can be found near the RNA but must be assisted by proximate and mobile cations. At distances larger than 16 A from the RNA center, a model of RNA as charged rod in a continuum of ionic solution provides quantitative description of the ion density (the same as in atomically detailed simulation). At shorter distances, the structure of RNA (and ions) has a significant impact on the pair correlation functions. Predicted binding sites of Mg(2+) at the RNA surface are in accord with structures from crystallography. Electric field relaxation is investigated. The relaxation due to solution rearrangements is completed in tens of picoseconds, while the contribution of RNA tumbling continues to a few nanoseconds.