L-type ultra-cool dwarfs are known to have a dusty atmosphere. Surface heterogeneities, due to cloud patterns or rotationally-induced oblateness, would result in an imperfect polarization cancellation and a small, but non-zero net polarization. The measurement of linear polarization could shed light on the dust distribution and oblateness of those objects, as well as the particle size distribution. Young brown dwarfs share many of their stellar counterparts' characteristics, including the presence of circumstellar disks. Dust scattering within the disk also leads to polarization, depending on the disk properties and inclination angle. We have obtained linear polarization observations for a sample of young and old brown dwarfs taken with FORS1 at the VLT. We present our measurements and compare our results with predictions from disk and photospheric models.