The grout injected into the joint with a primary velocity but solidifies gradually depending on the joint geometry and grout characteristics. Therefore the velocity changes completely, both in the perpendicular and in the injection direction. In the present study, the changes of two velocity components in the joints with various geometries are investigated using computational fluid dynamics (CFD) and finite volume numerical method. For this purpose joints are modeled as parallel smooth plates and the saw-tooth with different matednesses. The results show that velocity component in the injection direction of a joint with parallel smooth plates always reveal parabolic distribution towards the joint aperture. In the saw-tooth joint, velocity component in the injection direction increases in the narrowed locations and its profile changes from parabolic to undulated form. The velocity component perpendicular to injection direction in the joints with parallel smooth plates equals to zero from joint entry up to the point in which grout starts to solidify and after that point this component emerges and then changes. Vertical component of velocity is non-zero in the saw-tooth joint from joint entry and the changes both in quantity and direction depend on joint matedness, joint aperture ratio (k) and joint walls direction and dip.