In the forming section of a paper machine, a fiber suspension is flowing down onto a forming fabric, and a paper structure is formed. By using computer simulations this process can be studied, attaining new knowledge helping to improve paper quality and machine efficiency. In this thesis a suspension flow model is presented together with a simulation framework which is used to simulate early paper forming. Lay down simulations are performed, and the resulting sheets are compared with experiments. To properly resolve the frequent interactions between fibers, a physical interaction model has been developed. The suspension flow model consists of four sub-models: a fluid model, an object model, a fluid-object and object-fluid interaction model, and an object-object interaction model. The fluid model is based on the incompressible Navier-Stokes equations, and to capture the large motion and deformations of the fibers, a finite-strain beam model is used. The object’s effect on the fluid is calculated using a second-order accurate immersed boundary method, and the fluid’s effect on the fibers are resolved using an empirical drag force relation for cylinders. When a paper structure is formed the interactions between fibers are important. To resolve these interactions an object-object interaction model based on DLVO force has been developed. The model enables calculation of contact forces varying considerably over nanoscale distances without requiring the fiber time step to be reduced. In addition to the DLVO forces, a steric repulsion force has been developed handling the interaction taking place at the smallest separations including overlap. This work demonstrates the capacity of the presented framework, enabling computer simulations of the paper making process. Simulations are performed with thousands of fibers laying down onto a forming fabric, simultaneously resolving the complex interaction between fibers. For the simulated sheets with low density, the resulting air permeabilities agree well with experiments. When the density increases, the permeability of the simulated sheets does not decrease as much as in the experiments. This seems to be caused by some features missing in the current model. The fibers do not deform as tightly together as in the experiments, and the holes between fibers are not covered by fines. These features will be investigated in the future to improve the simulation framework further.