A modular fence system. The system includes fence planks designed for insertion into open channels of upper and lower fence rails. The fence rails are supported in a horizontal orientation between intermittent fence posts, with the fence planks extending vertically between the rails. The planks include resilient protrusions, called plank-projections, at their upper ends. The plank-projections are designed to engage with channel-projections formed in the open channels of the upper fence rail and lower fence rail, to inhibit inadvertent removal of the planks from the upper rail. Alternatively, the plank-projections may be eliminated in favor of having the channel-projections simply grip the planks frictionally, or, vice versa, the channel-projections could be eliminated in favor of having the plank-projections press frictionally against the walls of the open channels in the upper rail or lower rail or both. Accordingly, the engagement between the upper rail and the planks takes some weight off the lower rail such that fewer support posts are needed, and that engagement can be provided with just the channel-projections, or just the plank-projections, or both.