The objective of the present study is to analyze the laminar mixed convection in a square cavity with moving cooled vertical sidewalls. A constant flux heat source with relative length l is placed in the center of the lower wall while all the other horizontal sides of the cavity are considered adiabatic. The numerical method is based on a finite difference technique where the spatial partial derivatives appearing in the governing equations are discretized using a high order scheme, and time advance is dealt with by a fourth order Runge Kutta method. The Richardson number (Ri), which represents the relative importance of the natural and forced convection, is chosen as the bifurcation parameter. The effect of this non-dimensional number on the behavior of the fluid flow and the heat transfer is analyzed. Although the geometry and boundary conditions concerning the velocity and the temperature are symmetrical with respect to the vertical axis passing through the center of the cavity, the results show the existence of symmetric and asymmetric flow structures, varying according to the considered value of the Richardson number.