In this study, pattern formation at the bifurcation point from the quiescent state for free surface convection in circular containers is determined, A linearized instability calculation that employs three-dimensional disturbances in the presence of physically realistic side wall boundary conditions is made, The results of the present study will provide a very useful asymptotic limit for nonlinear numerical computations. Under restrictive conditions the current calculations check favorably with those of earlier workers, The results of these studies are compared with the experiments of Koschmieder and Prahl (J. Fluid Mech. 251, 571, 1990).