The band structure of hexagonal SiC polytypes has regions in the k-space where two or more energy bands are very close to each other. Tunneling of electrons (or holes) between bands due to a high electric field is one of the processes that may allow the electron to jump between energy bands. It is important to consider this effect in order to understand high-field transport properties in these polytypes. In this work we have used the two-band k·p approximation [1] to calculate the time-dependent tunneling probability for electron transitions between two bands using the approach of Krieger and Iafrate (KI) [2]. Electric field strengths between 0.1-4 MV/cm have been used to study the effect of tunneling. Drift times in the order of 10 fs have been considered, which is representative for the time between scattering events. We have applied the k·p approximation to different points in the Brillouin zone of 4H-SiC and proved that there is considerable tunneling between bands under realistic electric field strengths and scattering times.