A theory is developed to obtain the Weibull scale and shape parameters for in situ fibre strength utilizing the data obtained from a single-fibre-composite (SFC) test. It is well known that during the SFC test, the fibre fractures several times along its length at successive weak points that are randomly located. The SFC technique, although most commonly used for measuring the fibre/matrix interfacial shear strength, is an excellent way to determine the fibre flaw spacings a nd the in situ fibre failure stress at every fracture location. In the present technique, the SFC specimen is partitioned into a relatively large number of small sections of equal length such that each section will have either one or no fibre fracture point. Because all the sections may not include the fibre fracture points because of their random nature, the test data are regarded as "censored data". In other words, the theory is constructed for the estimation of Weibull parameters that takes into account the censored nature of the data. The Weibull parameters predicted using the present theory are in the same range as those obtained from the single fibre tension tests. For several reasons the values obtained from the SFC test tend to be slightly higher than those obtained from the simple tension tests. However, the in situ fibre strength values obtained using SFC technique may be more realistic and thus may be more useful in modelling composite strength.