The mechanical and electronic properties of GaP nanowires are investigated by computing the Young's modulus, Poisson's ratio, energy band gap and effective carrier masses using first-principles calculations based on density functional theory. The wurtzite structural nanowires with diameters upper limited to similar to 27 angstrom are strained by uniaxial strains in the range of -7.5-7.5%. The Young's moduli of nanowires are found to be decreased with increase of the size in the direction of the Young's modulus of the bulk GaP. The Poisson's effect is determined to be stronger in GaP nanowires than in the bulk. The energy band gaps of the unstrained and strained nanowires are obtained to be enlarged with decrease of the size due to the quantum size effect. The confinement effect is found larger in the compressed nanowires than in the stretched ones. All the unstrained nanowires except the largest one are indirect band gap materials. Indirect to direct band gap transition is determined to be size and strain dependent. The effective carrier masses in all unstrained nanowires are found small compared to the ones in the bulk GaP. The effective electron and hole masses are obtained to be modulated in nanowires of this work by the compressive and both compressive/tensile strains, respectively.