Geodetic networks have been observed for centuries with the designs based on intuition and empirical formulae. More recently, computer simulation has been pioneered in order to test networks prior to any observations being made. This involves the computation of the covariance matrix of the parameters from which the designer may determine whether or not the quality requirements of the prospective user are met. With the increasing cost of field operations it is becoming more important to find a set of observations that will meet the quality requirement whilst keeping costs to a minimum. Such a network is called an optimum network. The success'of the foregoing methods depends on the skill and experience of the designer. Accordingly, investigations have been carried out to determine the suitability of determining the optimal design of level networks. Four methods which solve the second order design problem to find the optimal design have been tested. These involve the Khatri-Rac matrix product to transform the problem into one which may be solved using either generalised matrix inverses or linear programming. In addition a way of automating the established simulation method of network design by removing observations using a criteria based on the relative error between stations, whilst considering the reliability of the network, is examined. The identification of the requirements of the user and their presentation in a form which is convenient for inclusion in mathematical models is also discussed. It is concluded that the particular methods of finding the optimal design via a solution to the second order design problem, which were investigated, are unsuitable. The automated simulation technique is, however, found to be succesful when applied to both small and large level networks and allows a great deal of flexibility with respect to different optimal criteria.