In this paper we investigate numerically chaotic behaviors of incompressible fluid flows at large Reynolds numbers in triangular driven cavities. The problem is first formulated as incompressible Navier-Stokes equations with appropriate boundary and initial conditions. The equations are then solved numerically by an exponentially fitted finite volume method for various Reynolds numbers up to 10(7). Numerical experiments on flows in triangular cavities with different depths are performed. The numerical results show clearly that the transitions of the flows from lamina to turbulence/chaos follow some conventional routes to chaos.