Injection of water into a rock formation through the flooding wells is a common practice to maintain reservoir pressure and increase ultimate recovery of hydrocarbons. While flowing through the well from surface to the rock formation, injected water typically transports fine particles, which are introduced either externally (untreated water) or internally (e.g., particles detached from the inner surface of a pipeline due to erosion and abrasion as well as mineral particles detached from pore surface). In the framework of the two-fluid approach, we formulate mathematical model for filtration of a particle-laden suspension in the vicinity of flooding wells. Two mechanisms affecting transport of non-colloidal fines are considered: trapping and mobilization. Trapped particles reduce permeability and porosity of the rock, which leads to the injectivity decline of the well. The model contains minimal set of tuning parameters describing particle trapping and mobilization rates. This is achieved by critical overview of existing models. We calibrate suspension filtration model against existing experimental (laboratory) data on fines mobilization and trapping in porous media. A parametric study of different flooding scenarios is carried out numerically. In particular, we investigate the effectiveness of periodic flooding regime, when the periods of injection are followed by flowback in order to wash out trapped fines from the near-wellbore zone and restore well injectivity. Implications to formation damage and cleanup phenomena peculiar to hydraulic fracturing and drilling are discussed. Practical recommendations are given.