  We study the interplay between a uniaxial strain and the topology of the
Haldane and the modified Haldane models which, respectively, exhibit chiral and
antichiral edge modes. The latter were, recently, predicted by Colom\'es and
Franz (Phys. Rev. Lett. {\bf 120}, 086603 (2018)) and expected to take place in
the transition metal dichalcogenides. Using the continuum approximation and a
tight-binding approach, we investigate the effect of the strain on the
topological phases and the corresponding edge modes. We show that the strain
could induce transitions between topological phases with opposite Chern numbers
or tune a topological phase into a trivial one. As a consequence, the
dispersions of the chiral and antichiral edge modes are found to be strain
dependent. The strain may reverse the direction of propagation of these modes
and eventually destroy them. This effect may be used for strain-tunable edge
currents in topological insulators and two-dimensional transition metal
dichalcogenides.
