We investigate the influence of a strong laser electromagnetic field on the α-decay rate by using the Hennenberger frame of reference. We introduce an adimensional parameter D=S_{0}/R_{0}, where R_{0} is the geometrical nuclear radius and S_{0}∼sqrt[I]/ω^{2} is a length parameter depending on the laser intensity I and frequency ω. We show that the barrier penetrability has a strong increase for intensities corresponding to D>D_{crit}=1, due to the fact that the resulting Coulomb potential becomes strongly anisotropic even for spherical nuclei. As a consequence, the contribution of the monopole term increases the barrier penetrability by 2 orders of magnitude, while the total contribution has an effect of 6 orders of magnitude at D∼3D_{crit}. In the case of deformed nuclei, the electromagnetic field increases the penetrability by an additional order of magnitude for a quadrupole deformation β_{2}∼0.3. The influence of the electromagnetic field can be expressed in terms of a shifted Geiger-Nuttal law by a term depending on S_{0} and deformation.