  Parallax measurements of pulsars allow for accurate measurements of the
interstellar electron density and contribute to accurate tests of general
relativity using binary systems. The Square Kilometre Array (SKA) will be an
ideal instrument for measuring the parallax of pulsars, because it has a very
high sensitivity, as well as baselines extending up to several thousands of
kilometres. We performed simulations to estimate the number of pulsars for
which the parallax can be measured with the SKA and the distance to which a
parallax can be measured. We compare two different methods. The first method
measures the parallax directly by utilising the long baselines of the SKA to
form high angular resolution images. The second method uses the arrival times
of the radio signals of pulsars to fit a transformation between time
coordinates in the terrestrial frame and the comoving pulsar frame directly
yielding the parallax. We find that with the first method a parallax with an
accuracy of 20% or less can be measured up to a maximum distance of 13 kpc,
which would include 9,000 pulsars. By timing pulsars with the most stable
arrival times for the radio emission, parallaxes can be measured for about
3,600 millisecond pulsars up to a distance of 9 kpc with an accuracy of 20%.
