III-nitrides GaN and InN, and In (x) Ga1-x N solid solutions are polarizable semiconductors that crystallize in the prototypical wurtzite (W) structure. We present here the results of a density functional theory study carried out to determine the spontaneous polarization, piezoelectric coefficients, and elastic coefficients of In (x) Ga1-x N alloys as a function of In the concentration x. To calculate these properties, we construct three distinct hexagonal/orthorhombic equivalent In (x) Ga1-x N supercells that are derived from the disordered W unit cell of GaN and InN. These include an ordered W lattice (P6(3) mc/Pmc2(1)) and orthorhombic O-16 and O-32 lattices with Pmn2(1)/Pna2(1) or P2(1) symmetry, respectively. Depending on the crystal structure, spontaneous polarization as a function of the In concentration x shows a downward bowing (W), a linear interpolation (O-16), and an upward bowing (O-32) between -0.033 C/m(2) and -0.043 C/m(2), the spontaneous polarizations of the end components GaN and InN, respectively. The composition dependence of the effective basal plane and out of plane (along the [0001] direction) piezoelectric coefficients (e (//) and e (33), respectively) in the W and O-16 structure is non-linear and varies between e (//) = -0.287 C/m(2) and e (33) = 0.598 C/m(2) for GaN, and e (//) = -0.455 C/m(2) and e (33) = 1.044 C/m(2) for InN. While the bulk modulus of In (x) Ga1-x N in the W and O-16 structures follows Vegard's law from 170 GPa (x = 0) to 124 GPa (x = 1), in the O-32 structure it shows a strong downward bowing for compositions 0 < x < 0.5.