  We describe an assembly of numerical tools to model the output data of the
Planck satellite. These start with the generation of a CMB sky in a chosen
cosmology, add in various foreground sources, convolve the sky signal with
arbitrary, even non-symmetric and polarised beam patterns, derive the time
ordered data streams measured by the detectors depending on the chosen
satellite-scanning strategy, and include noise signals for the individual
detectors and electronic systems. The simulation products are needed to
develop, verify, optimise, and characterise the accuracy and performance of all
data processing and scientific analysis steps of the Planck mission, including
data handling, data integrity checking, calibration, map making, physical
component separation, and power spectrum estimation. In addition, the
simulations allow detailed studies of the impact of many stochastic and
systematic effects on the scientific results. The efficient implementation of
the simulation allows the build-up of extended statistics of signal variances
and co-variances.
  Although being developed specifically for the Planck mission, it is expected
that the employed framework as well as most of the simulation tools will be of
use for other experiments and CMB-related science in general.
