In this thesis, we aim to study the sampling allocation problem of survey statistics under uncertainty. We know that the stratum specific variances are generally not known precisely and we have no information about the distribution of uncertainty. The cost of interviewing each person in a stratum is also a highly uncertain parameter as sometimes people are unavailable for the interview. We propose robust allocations to deal with the uncertainty in both stratum specific variances and costs. However, in real life situations, we can face such cases when only one of the variances or costs is uncertain. So we propose three different robust formulations representing these different cases. To the best of our knowledge robust allocation in the sampling allocation problem has not been considered so far in any research. The first robust formulation for linear problems was proposed by Soyster (1973). Bertsimas and Sim (2004) proposed a less conservative robust formulation for linear problems. We study these formulations and extend them for the nonlinear sampling allocation problem. It is very unlikely to happen that all of the stratum specific variances and costs are uncertain. So the robust formulations are in such a way that we can select how many strata are uncertain which we refer to as the level of uncertainty. We prove that an upper bound on the probability of violation of the nonlinear constraints can be calculated before solving the robust optimization problem. We consider various kinds of datasets and compute robust allocations. We perform multiple experiments to check the quality of the robust allocations and compare them with the existing allocation techniques.