This study presents a mathematical model for the injection of Bingham fluid as common grout material into a horizontal slot formed between parallel plates. The proposed model consisted of a grout reservoir model, a slot model, and an intermediate model that bridged the former two models. The authors showed that it is necessary to include a grout reservoir model in the injection model to avoid singularity of velocity when the grout penetration length is zero. This approach also allowed investigation of the initial stage flow condition during the injection process, especially at the inlet of the slot. Based on the proposed model, the approximate solution for the grout penetration length at the initial stage of injection was also derived. The performance of the proposed model was compared against a well-established model under laminar flow condition.