We present deep V and I photometry for the open cluster NGC 4815 and four surrounding Galactic fields down to a limiting magnitude V ~ 25. These data are used to study cluster spatial extension by means of star counts, and to derive the luminosity (LF) and mass function (MF). The radius turns out to be 3.6+/-0.3 arcmin at V=19.0, whereas the mass is 880+/-230 msun down to V=20.8. From the color-magnitude diagram, we obtain the LFs in the V and I bands, using both the standard histogram and an adaptive kernel. After correction for incompleteness and field star contamination, the LFs were transformed into the present day mass functions (PDMF). The PDMFs from the V and I photometry can be represented as a power-law with a slope alpha = 3.1+/-0.3 and alpha = 2.9+/-0.3 (the (Salpeter \cite{salp55}) MF in this notation has a slope alpha = 2.35) respectively, in the mass range 2.5 <= (m)/(msun) <= 0.8. Below this mass, the MF cannot be considered as representative of the cluster IMF, as it is the result of the combined effect of strong irregularities in the stellar background, probable internal dynamical evolution of the cluster and/or interaction of the cluster with the dense Galactic field. Unresolved binaries and mass segregation can only flatten the apparent derived IMF, so we expect that the real IMF must be steeper than the quoted slope by an unknown amount. Based on observations made at the European Southern Observatory, La Silla, Chile.