Our main aim in this thesis is to obtain an elicitation method for quantifying uncertainty about a population distribution with uncertain mean and variance. An example of where this methodology could be used is in risk analysis, where experts are uncertain about values of input parameters in a mechanistic model and with little or no data available. In addition, it could be used to obtain a prior distribution in Bayesian inference. In this thesis, we first search the literature of elicitation, since the review of O'Hagan et al. (2006), aiming to identify best elicitation practice. We then investigate the previous elicitation methods that can be used for quantifying uncertainty in our problem. The previous methods ask experts to update their judgements using Bayes' theorem, but experts may not do that correctly. Additionally, we propose modifications on the previous methods in an attempt to overcome their limitations in practice. We propose a new elicitation method that attempts to avoid the potential limitations of the previous methods. We extend the elicitation problem by quantifying uncertainty about a normal distribution, a log-normal distribution, and a logit-normal distribution. In addition, we aim to develop a new feedback plot that allows the experts to clearly visualise the effect of their judgements about the prior distributions of the population mean and variance into the fitted population distribution. Moreover, we develop an interactive software tool for implementing the proposed method in practice. We then illustrate and validate the use of the proposed method in practice through a real elicitation exercise.