Cost estimation is an expensive and time consuming element of a company's tendering process. The purpose of this study is to reduce the time, and consequently the cost, required to estimate the price of chemical process vessels from the current days or weeks to minutes or seconds. Traditional cost estimation involves calculating the amount ofinetal required, the numberof metres ofwelding, the manhours involved, and soon. Here, more recent methods are explored, involving the relationship between a vessel's overall specification and its price. Hence, a database of costed vessels can be used to find the cost ofproposed new vessels by examining these relationships and applying not only hard and fast mathematical rules, but also more intuitive links. Regression analysis is used to establish a base line by which to judge recent techniques such as neural networks, fuzzy matching, rational polynomials and non-linear functions. Each of the methods is applied to a set ofindustrial data, raising the supplementary 'real world' issue covered here - the constraint of having only a relatively small data set. This in turn leads to the exploration ofprincipal component analysis in order to reduce the number ofparameters required. The resultss howt hatt hem odernm ethodsp, articularly (simple)n euraln etworksa ndr ational equationsh avemuchtoo ffer,w hilstbeingq uick ande asytoi mplement,t heyg enerallyproduce results within the range expected of initial estimates. Some of the techniques described are currently being used by the industrial sponsor on an experimental basis and could also be applied to other areas where a cost database exists