Abstract <p>We theoretically studied and observed the photoionization rates of the alkali and noble atoms driven by an elliptically polarized Ti:sapphire laser for the barrier suppression ionization scheme. We extended the barrier suppression ionization formula developed by Posthumus and coworkers by considering the inclusion of the initial momentum of the ejected photoelectrons and the ponderomotive potential and Stark shift in unperturbed ionization potential. The extended formula is applied to both groups of atoms and the obtained results are compared with those obtained by the initial formula with the aim to determine the influence of all mentioned effects. Additionally, we explored the influence of the field’s ellipticity on the barrier suppression ionization rate. We found that it is sensitive to the change of the field ellipticity and the inclusion of all mentioned effects as well.</p>