The vertical expansion of fractures during hydraulic fracturing in low-permeability bottom-water oil and gas reservoirs is a crucial factor that significantly influences stimulation effectiveness. Fractures propagate concurrently in three dimensions; however, as operation time for fracturing and fracture length increase, there is gradual reduction in fracture height. In absence of a barrier layer or with inadequate strength and thickness, fractures may extend vertically or oscillate through it leading to an “unyielding” fractured state which impedes successful operations. This study introduces a mathematical model delineating the vertical expansion of hydraulic fractures while computing stress intensity factors at both upper and lower tips of each individual fracture. We utilize numerical methods to examine how vertical heterogeneity within reservoir rocks impacts laws governing vertical fracture propagation while conducting sensitivity analysis for making informed decisions on design parameters for hydraulic fracturing operations. The research results show that an escalation in stress disparity as well as increased toughness results into diminished height for hydraulic fractures. Hydraulic fracturing augments fracture lengths along their respective axes. Nevertheless, if gap stress disparity surpasses net fluid pressure, then there’s reduction observed in fracture lengths. With an increasing ratio between local stress gradient versus fluid gravity gradient, hydraulic fractures persistently advance vertically across cap as well as bed formations.