The plasma sheet pressure and its spatial structure during the substorm growth phase are crucial to understanding the development and initiation of substorms. In this paper, we first statistically analyzed the growth phase pressures using Geotail and THEMIS data, and identified that solar wind dynamic pressure (PSW), energy loading, and sunspot number as the three primary factors controlling the growth phase pressure change. We then constructed a 2D equatorial empirical pressure model and an error model within r ≤ 20 RE using the Support Vector Regression Machine (SVRM) with the three factors as input. The model predicts the plasma sheet pressure accurately with median errors of 5%, and predicted pressure gradients agree reasonably well with observed gradients obtained from two-probe measurements. The model shows that pressure increases linearly as PSW increases, and the PSW effect is stronger under lower energy loading. However, the pressure responses to energy loading and sunspot number are nonlinear. The pressure increases first with increasing loading or sunspot number, then remains relatively constant after reaching a peak value at ~8000 kV∙min loading or sunspot number of ~80. The loading effect is stronger when PSW is lower and the pressure variations stronger near midnight than away from midnight. The sunspot number effect is clearer at smaller r. The pressure model can also be applied to understand the pressure changes observed during a substorm event by providing evaluations of the effects of energy loading and PSW, as well as the temporal and spatial effects along the spacecraft trajectory.