In this paper we set out how a wealth tax might be administered in practice, how a system of returns, valuation, assessment and payment might work and describe some of the challenges which the UK tax authority (HMRC) would face in maintaining an adequate level of collection. In Section 1 we set out some of the principles of tax administration, before turning to examine the administration of existing taxes on wealth (in the UK and overseas) in Section 2. Section 3 describes the various elements of tax administration and the issues and choices that the administration of a wealth tax would need to address. In Section 4 we examine tax leakage, the various potential areas of tax loss and the likely size of the tax gap for a wealth tax. Section 5 considers the investigation and enforcement of a wealth tax by HMRC and the tools and powers that it might need.