  We give a classification of the log canonical models of elliptic surface
pairs consisting of an elliptic fibration, a section, and a weighted sum of
marked fibers. In particular, we show how the log canonical models depend on
the choice of the weights. We describe a wall and chamber decomposition of the
space of weights based on how the log canonical model changes. In addition, we
give a generalized formula for the canonical bundle of an elliptic surface with
section and marked fibers. This is the first step in constructing
compactifcations of moduli spaces of elliptic surfaces using the minimal model
program.
