By plane
By plane
Flights from Moscow are a few times a week on Rusline. There are more regular flights to Volgograd and Rostov, with transfer to Elista by bus or train respectively.
By train
By train
The Moscow-Elista train route goes through Stavropol. However, the most convenient way is travel to Volgograd by train then on to Elista by express minivan, which are relatively cheap.
By bus
By bus
Several private companies operate a daily bus service between Moscow and Elista. The pickup point in Moscow is Luzhniki Stadium. A one-way ticket costs about 1350RUR.