On the base of published theoretical evolutionary tracks of stars of
various masses the modeling of color-magnitude diagram of Praesepe
cluster was performed. Computer program created for this purpose allows
to build color-magnitude diagrams and luminosity functions of model
clusters in the presence of double stars, dispersion of ages of
cluster stars and their pre-main-sequence evolution. By the comparison
of observed color-magnitude diagram with model one it was shown that
inclusion of these effects is enough to interpret the structure of
color - magnitude diagram of Praesepe cluster. The age dispersion of
cluster stars of turn-off point mass is appear to be equal to
8 x 107 years. The fraction of double stars between cluster members
is equal to 20%, the distribution of mass ratios q of double stars'
components is uniform for q > 0.4 with marked deficiency of systems with
smaller q. The letter allow to estimate the fraction of double stars by
the direct star counts on the color-magnitude diagram.