The problem of obtaining an analytical expression for the tunnel-diode static characteristic is best approached using essentially a curve-matching technique. Two types of expressions are possible:(a) a simple expression (one or two terms only) which can be used in analytical studies(b) a complex expression suitable for computer manipulation.The error can be held to ±10% of the peak current using the type (a) approach, and details are given. Greater accuracy is possible with the type (b) approach, and examples are given in which a ±2% error is obtained using a ninth-order polynomial for a gallium arsenide diode; an error of ±5% is obtained using a seventh-order polynomial for a germanium diode.Using a reduction method and the type (b) expression, it is shown that representation of the static characteristics up to the valley voltage is possible using a quartic expression, the error being ±10%. This result is important in view of the number of attempts which have been made to achieve a match with a low-order polynomial. The quartic expression can be derived directly using Lagrange's interpolation formula.The error from the type (a) approach is small, and it is expected that this approach will be entirely adequate for the solution of engineering problems.