This paper deals with growth of injection hydrofractures in transient linear flow in a low permeability, soft rock. Seventeen waterflood injectors in Section 12 of the Middle Belridge diatomite, three steam injectors in Section 29 of the South Belridge diatomite, as well as forty four injectors in the Lost Hills I waterflood have been analyzed. The field data show that cumulative injection of water or steam scales with time to the power of 1, rather than ½ predicted from the theory of linear transient flow. In other words, at constant injection pressure, injection rate is remarkably constant. Therefore, either the injection hydrofractures grow with time, or the formation permeability increases with time, or both. A simple mass balance of hydrofracture growth during fluid injection, attributed to Carter, is corrected, extended to the case of variable injection pressure, and presented in a simplified form. The growth of fracture area at constant injection rate is expressed in terms of two easily measured field parameters, the early “injection slope” in linear transient flow, and the average injection rate. Carter’s fracture growth rate is further halved to account for the reservoir layer homogeneity parallel and perpendicular to the hydrofracture plane. The Carter theory predictions are then compared with the growth rate of hydrofracture area calculated independently for two steam injectors in Section 29. There is remarkable agreement between the modified Carter theory predictions and the independently estimated rates of growth of these two hydrofractures. We show that fluid injection above a reasonable minimum rate must lead to hydrofracture extension if injection pressure is bounded from above. Ultimately, fracture growth is inevitable, regardless of mechanical design of injection wells and injection policy. We also show that water injection leads to less severe formation damage and fracture extension than steam. By analyzing the thermal and pore stresses, we demonstrate that steam injection may lead to the creation of horizontal fractures, vertical fracture extension, and reservoir damage. Better control of steam injection is, therefore, a must. We address the optimal injection control strategy in Part 2 of this paper.