[110] 60 degrees and [100] edge misfit dislocations in In0.06Ga0.94As heterostructures grown on patterned GaAs (001) substrates with relatively low misfit f(f=0.0043) have been investigated. The reduction of [110] misfit dislocation density on mesas is observed by cathodoluminescence, while the [100] misfit dislocation density on mesas observed by synchrotron radiation double crystal topography remains unchanged. The critical thickness is calculated by modifying the Matthews mechanical equilibrium theory introduced by Chidambarrao et al. The calculated results can be applied to both the nonpatterned area and the sidewalls of the mesa. The critical thickness of one side of the mesa is larger than that of nonpatterned areas. The critical thickness of both sides of mesas is dependent on the angle between the sidewall and (001) GaAs. This is likely due to different values of cos phi/sin psi, which determines the values of the friction force F-F With different sidewall angles. It is suggested that the [100] misfit dislocations are generated by climb and they can cross mesas by climbing along [100] directions.