This paper investigates the multivariate support of forward Libor rates in the onefactor, constant volatilities Libor market model. The comparatively simple bivariate case was solved in Jamshidian (2008) in connection to the recent finding by Davis and Mataix-Pastor (2007) of positive probability of negative Libor rates in the swap market model. The approach here builds on Jamshidian (2008) but becomes really effective only in the trivariate case, and there particularly for a special “flat-volatility‿ case, leading to an analytic solution. The main idea is a certain recursion in the Libor market model bymeans of which the calculation of the support is reduced to a calculus of variation problem (with bounds on the slope).