Pore pressure/stress coupling is the change in the smaller horizontal stress σh associated with changes in pore pressure P, and has been measured in numerous reservoirs worldwide. These measurements suggest that the change in minimum horizontal stress Δσh is on average ca. 64% of the change in the reservoir pore pressure ΔP, but can be as low as 34% and as high as 118%. Conventionally it is assumed that the total vertical stress σv, given by the overburden, is not affected by changes in pore pressure, in contrast to the horizontal stresses σH and σh. We investigate analytically and numerically the spatio-temporal pore pressure and stress evolution in poroelastic media for continuous fluid injection at a point source, and calculate from the numerical modelling results the ratio Δσ/ΔP. Analytically, we show that the measured average of Δσh/ΔP can mathematically be deduced from the long-term limit of the spatio-temporal evolution of pore pressure and horizontal stress caused by fluid injection at a point source. We compare our numerical results to the analytical solution for continuous point injection into homogeneous poroelastic media as well as to Δσh/ΔP values measured in the field, and show that all stress components change with a variation in P. We use the concept of poroelasticity to explain the observed coupling between pore pressure and stress in reservoirs, and we consider different measurement locations and measurement times as one possible reason for the measured variation in Δσh/ΔP in different oil fields worldwide.