South Africa dominated day one of the first Test match against Bangladesh at Senwes Park in Potchefstroom on Thursday.
At stumps, the Proteas were 298 for 1 in 90 overs.
Opener Elgar was not out on 128 while Hashim Amla scored unbeaten 68 runs.
Earlier, Bangladesh Test skipper Mushfiqur Rahim won the toss and invited South Africa to bat first.
Bangladesh: 1 Tamim Iqbal, 2 Imrul Kayes, 3 Mominul Haque, 4 Mahmudullah, 5 Mushfiqur Rahim (capt), 6 Liton Das (wk), 7 Sabbir Rahman, 8 Mehidy Hasan, 9 Taskin Ahmed, 10 Shafiul Islam, 11 Mustafizur Rahman.
South Africa: 1 Dean Elgar, 2 Aiden Markram, 3 Hashim Amla, 4 Temba Bavuma, 5 Faf du Plessis (capt), 6 Quinton de Kock (wk), 7 Andile Phehlukwayo, 8 Keshav Maharaj, 9 Kagiso Rabada, 10 Morne Morkel, 11 Duanne Olivier.