The time-dependent deformation in rocks is closely associated with the growth, interaction and coalescence of pre-existing micro-cracks. Initially, when the constant load is applied, the cracks propagate sub-critically and expected to fail rapidly upon reaching critical stress. The velocity of subcritical crack propagation is one of the important parameters in crack growth. Its relation to the stress intensity is studied by many researchers. Whereas, studies are mostly confined to Mode I failure. Subcritical crack growth of rock having pre-existing non-persistent narrow flaw is not fully explored, which can resemble micro-crack behaviour under long term loading. Details on the effect of corresponding flaw angle, stress level, and confinement on subcritical crack propagation are not documented well. Proposed study aims to improve the understanding of time-dependent rock failure behaviour with pre-existing non-persistent narrow flaws through laboratory experiments and numerical modelling. This proposal covers the detailed literature review against the proposed objective on the crack growth behaviour in rock-like material with pre-existing non-persistent narrow flaws under uniaxial and biaxial creep loading. The proposed methodology with step by step procedure to be adopted to carry out this research will be discussed.