  Measurements of redshift space distortions (RSD) provide a means to test
models of gravity on large-scales. We use mock galaxy catalogues constructed
from large N-body simulations of standard and modified gravity models to
measure galaxy clustering in redshift space. We focus our attention on two of
the most representative and popular families of modified gravity models: the Hu
\& Sawicki $f(R)$ gravity and the normal branch of the DGP model. The galaxy
catalogues are built using a halo occupation distribution (HOD) prescription
with the HOD parameters in the modified gravity models tuned to match with the
number density and the real-space clustering of {\sc boss-cmass} galaxies. We
employ two approaches to model RSD: the first is based on linear perturbation
theory and the second models non-linear effects on small-scales by assuming
standard gravity and including biasing and RSD effects. We measure the monopole
to real-space correlation function ratio, the quadrupole to monopole ratio,
clustering wedges and multipoles of the correlation function and use these
statistics to find the constraints on the distortion parameter, $\beta$. We
find that the linear model fails to reproduce the N-body simulation results and
the true value of $\beta$ on scales $s < 40\Mpch$, while the non-linear
modelling of RSD recovers the value of $\beta$ on the scales of interest for
all models. RSD on large scales ($s\gtrsim20$-$40\Mpch$) have been found to
show significant deviations from the prediction of standard gravity in the DGP
models. However, the potential to use RSD to constrain $f(R)$ models is less
promising, due to the different screening mechanism in this model.
