We present new high angular resolution observations of the ^ { 13 } CO 1 \rightarrow 0 rotational line towards the HBe star R Mon , obtained with the IRAM Bure Interferometer , along with the previous results in the observed transitions ^ { 12 } CO 1 \rightarrow 0 and 2 \rightarrow 1 . We have used a flat disk model to fit the ^ { 12 } CO 1 \rightarrow 0 and 2 \rightarrow 1 , and ^ { 13 } CO 1 \rightarrow 0 emission , in a strip perpendicular to the outflow axis . The model assumes standard abundances ( X ( ^ { 12 } CO ) = 8 \cdot 10 ^ { -5 } , X ( ^ { 13 } CO ) = 9 \cdot 10 ^ { -7 } ) , radial potential temperature and density laws ( T ( K ) = T _ { o } r ^ { - q } , \rho ( cm ^ { -3 } ) = \rho _ { o } r ^ { - p } ) , and Local Thermodynamic Equilibrium . The ^ { 13 } CO and ^ { 12 } CO emission is consistent with a flat disk at an inclination angle of 20 ^ { \circ } in Keplerian rotation around the star . The gaseous disk is fitted with a mass of 0.014 M _ { \odot } , an outer radius of 1500 AU , a temperature of 4500 K at the inner radius ( 1 AU ) , and values of q=0.62 and p=1.3 for the indexes of the temperature and density laws . This new ^ { 13 } CO observations allow us to conclude that the disk around R Mon is flat . Our result confirms previous works suggesting a predominant flat geometry in disks around early Be stars .