  The Szekeres inhomogeneous models can be used to model the true lumpy
universe that we observe. This family of exact solutions to Einstein's
equations was originally derived with a general metric that has no symmetries.
In this work, we develop and use a framework to integrate the angular diameter
and luminosity distances in the general Szekeres models. We use the affine null
geodesic equations in order to derive a set of first-order ordinary
differential equations that can be integrated numerically to calculate the
partial derivatives of the null vector components. These equations allow the
integration in all generality of the distances in the Szekeres models and some
examples are given. The redshift is determined from simultaneous integration of
the null geodesic equations. This work does not assume spherical or axial
symmetry, and the results will be useful for comparisons of the general
Szekeres inhomogeneous models to current and future cosmological data.
