Fingerprint classification consists of labeling a fingerprint impression as one of several major types of fingerprints arch, left loop, right loop, whorl, etc. The problem of fingerprint matching amounts to deciding whether or not two impressions were produced by the same finger. We propose a model based method for fingerprint classification which only uses the flow field, avoiding the non-trivial computation of the thinned ridges and minutia points. For each class, a fingerprint kernel is defined, which models the shape of fingerprints in that class. The classification is then achieved by finding the kernel that best fits the flow field of the given fingerprint. We obtain a classification accuracy of 91.25% on the NIST 4 database. We also show how the kernel fitting procedure can be used for fingerprint alignment.