  In this first paper of the series we describe our project to calibrate the
distance determination method based on early-type binary systems. The final
objective is to measure accurate, geometrical distances to galaxies beyond the
Magellanic Clouds with a precision of 2%. We start with the analysis of two
early-type systems for which we have collected all the required spectroscopic
and photometric data. Apart from catalog publications, these systems have not
been studied yet, and it is the first time the modeling of light and radial
velocity curves is performed for them. From the analysis we obtained precise
physical parameters of the components, including the masses measured with
precision of 0.6-1% and radii with precision of 0.4-3%. For one system we
determined the $(V-K)$ color and estimated the distance using the bolometric
flux scaling method (DM=18.47 $\pm$ 0.15 mag), which agrees well with our
accurate determination of the distance to the LMC from late-type giants. For
the same system we determined the surface brightness of individual stars using
our model, and checked that it is consistent with a recent surface brightness
-- color relation. We compared our results with evolution theory models of
massive stars and found they agree in general, however, models with higher
overshooting values give more consistent results. The age of the system was
estimated to from 11.7 to 13.8 Myr, depending on the model.
