In this communication, we show how asteroids observations from the Gaia mission can be used to perform local tests of General Relativity (GR). This ESA mission, launched in December 2013, will observe --in addition to the stars-- a large number of small Solar System Objects (SSOs) with unprecedented astrometric precision. Indeed, it is expected that about 360,000 asteroids will be observed with a nominal sub-mas precision. Here, we show how these observations can be used to constrain some extensions to General Relativity. We present results of SSOs simulations that take into account the time sequences over 5 years and geometry of the observations that are particular to Gaia. We present a sensitivity study on various GR extensions and dynamical parameters including: the Sun quadrupolar moment $J_2$, the parametrized post-Newtonian parameter $beta$, the Nordtvedt parameter $eta$, the fifth force formalism, the Lense-Thirring effect, a temporal variation of the gravitational parameter $GM_textrm{sun}$ (a linear variation as well as a periodic variation), the Standard Model Extension formalism,... Some implications for planetary ephemerides analysis are also briefly discussed.
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