Non-parametric procedures are often used for the analysis of pharmacokinetic trials. Fewer design procedures are available for non-parametric estimation than for parametric estimation. Linear interpolation is widely used for curve estimation in pharmacokinetic trials, where often only sparse sampling is feasible. Current design procedures for smoothing or local fit are not suitable as they are based on asymptotic properties and the bias of the estimate is ignored. This paper proposes optimal designs that minimize the mean squared error of linear interpolation. Optimal designs for three situations are considered. The first situation is single curve estimation based on an ordinary non-linear model. The second is estimating several curves in a non-linear mixed model setting using an average mean squared error as the design criterion. The third situation is destructive sampling where estimating the average curve is the main purpose. In the first situation, the design results in the best linear interpolation when the variance is constant. For the destructive sampling design, an algorithm based on approximations is proposed. This algorithm can be programmed in a common statistical package. Numerical examples are used to illustrate the design procedure.