Reasons for the shape include:

#A round manhole cover cannot fall through its circular opening, whereas a square manhole cover may fall in if it were inserted diagonally in the aperture (A Reuleaux triangle or other curve of constant width would also serve this purpose, but round covers are much easier to manufacture.)
#Round tubes are the strongest and most material-efficient shape against the compression of the earth around them, and so it is natural that the cover of a round tube assume a circular shape.
#The bearing surfaces of manhole frames and covers are machined to assure flatness and prevent them from becoming dislodged by traffic. Round castings are much easier to machine using horizontal boring mills.
#Circular covers do not need to be rotated to align them when covering a circular manhole.
#Human beings have a roughly circular cross-section.
#A round manhole cover can be more easily moved by being rolled.
#It's easier to dig a circular hole.
#Supply. Most manhole covers are made by a few large companies. A different shape would have to be custom made