In this paper, we consider the obstacle problem for the inhomogeneous 𝑝-Laplace equation

$$\mathrm{div}(\nabla u|^{p-2}\nabla u)=f\cdot p\chi\{u>0\},\quad 1 < p < 2,$$

where 𝑓 is a positive, Lipschitz function. We prove that the free boundary has finite $(N-1)$-Hausdorff measure and stability property, which completes previous works by Caffarelli (J. Fourier Anal. Appl. 4(4--5) (1998) 383--402) for $p=2$, and Lee and Shahgholian (J. Differ. Equ. 195 (2003) 14--24) for $2 < p < \infty$.

In this paper, we establish growth rate of solutions near free boundaries in the identical zero obstacle problem for quasilinear elliptic equations. As a result, we obtain porosity of free boundaries, which is naturally an extension of the previous works by Karp et al. (J. Diff. Equ. 164 (2000) 110–117) for 𝑝-Laplacian equations, and by Zheng and Zhang (J. Shaanxi Normal Univ. 40(2) (2012) 11–13, 18) for 𝑝-Laplacian type equations.