A neural network model that produces many of the directional and spatial response properties that have been observed for motor cortical neurons in monkeys moving towards targets in space is described. These include motor cortex nodes with broad tuning in a single preferred direction, approximately linear variation in activity for different hold positions, and approximate invariance in preferred direction for different points in space. The model is also compatible with population analyses performed on motor cortical neurons. Across nodes, the distribution of preferred directions is uniformly distributed in directional space, and the degree of tuning and response magnitude vary from node to node. A population code used to predict accurately the direction of arm movements from a large population of coarsely tuned individual neurons also works using a simulated population of responses obtained from the neural network model. This code works for different starting locations in space using the same parameters. Thus, this network model provides a first step in understanding how neural activity patterns in the motor cortex might be generated.