The Sitter's Practise is one of the Thirteen Ascetic Practices.
It is practised by some forest monks, but it is allowed to sleep without lying down. I tried it a few times for a single night at Wat Pah Nanachat and Chithurst, but always found it counter-productive. There are three grades:
This is from the Path of Purification:
73. xiii. The sitter’s practice is undertaken with one of the following statements: “I refuse lying down” or “I undertake the sitter’s practice.”
The sitter can get up in any one of three watches of the night and walk up and down: for lying down is the only posture not allowed. These are the directions. 
74. This has three grades too. Herein, one who is strict is not allowed a back-rest or cloth band or binding-strap [to prevent falling while asleep].17 The medium one is allowed any one of these three. The mild one is allowed a back-rest, a cloth band, a binding-strap, a cushion, a “five-limb” and a “seven-limb.” A “five-limb” is [a chair] made with [four legs and] a support for the back. A “seven-limb” is one made with [four legs,] a support for the back and an [arm] support on each side. They made that, it seems, for the Elder Pìþhábhaya (Abhaya of the Chair). The elder became a non-returner, and then attained Nibbána.
• • • • (Upasampadā: 24th June, 1979)