We study the effects of periodic driving on a variant of the Bernevig-Hughes-Zhang (BHZ) model defined on a square lattice. In the absence of driving, the model has both topological and non-topological phases depending on the different parameter values. We also study the anisotropic BHZ model and show that, unlike the isotropic model, it has a non-topological phase which has modes localized on only two of the four edges of a finite sized square. When an appropriate term violating time-reversal symmetry is added, the edge modes get gapped and gapless states appear at the fourcorners of a square. When the system is driven periodically by a sequence of two pulses, multiple corner states may appear depending on the driving frequency and other parameters. We discuss to what extent the system can be characterized by topological invariants such as the Chern number and mirror winding number. We have shown that the locations of the jumps in these invariants can be understood in terms of the Floquet operator at one of the time-reversal invariant momenta.