A process and an apparatus are provided for producing pulp from lignocellulosic material by an alkaline cooking process, in which process preheated chips are treated in an impregnation stage with impregnation liquor, which is taken from the impregnation stage, and concentrated to obtain both a high inorganic and organic dry solid content. The temperature is higher than in the heating of the chips and in the removal of air, and is sufficient to enable the finishing of the reactions in the impregnation stage before the cooking stage. The majority of the alkali is added to the impregnation stage. In the cooking stage alkali is added to enable the delignification to be performed to a desired degree, and at the end of the cook black liquor is added to regulate the liquid-to-wood ratio. The process can be applied both to a continuous cook and to a batch cook.