The present research work undertakes the study of the initiation and propagation of cracks in brittle material emanating from indentation loading by means of phase-field method (PFM) with staggered algorithm and hybrid formulation. Among numerous methodologies, PFM is an encouraging tool for tackling problems of cracks initiation and propagation from an originally undamaged solid submitted to compression induced by the contact of a rigid indenter. The simulation indicates that crack initiates outside the contact region due to the compressive hydrostatic pressure in the contact region. The propagation direction ϕ in the cases of slip and rough contacts for flat and cylindrical indenters was influenced by Poisson ratio value V, with larger V leading to smaller ϕ. The obtained results accord well with those experimentally mentioned in the literature.