Standard geostatistical techniques provide effective methods for estimating the global abundance and precision of a variable of interest, for mapping its spatial distribution and for describing its spatial structure. In the case of acoustic survey data, however, obtaining a measure of precision of the global abundance estimate is confounded by the combination of variances from the interpolation of both the acoustic data and the concomitant fish length data. Even if the global estimation variance could be calculated, the distribution of the estimation error is not known and so confidence intervals cannot be determined. Furthermore, kriged distribution maps, in minimising the estimation variance, tend to smooth out local details of the attribute’s spatial variation: small values can be overestimated and larger ones underestimated, such that the kriged map is smoother than reality. This can lead to serious shortcomings when trying to detect patterns of extreme attribute values, such as the high densities encountered in some fish schools. Stochastic geostatistical simulations, conditional on sampled locations, provide a solution to many of these problems. They can deliver a measure of uncertainty for local (density) estimates, a confidence interval estimation for the global mean density, and finally, reproduce global statistics, such as the sample histogram and variogram. In so doing, they also provide maps of the attribute, which are spatially realistic because the variogram is reproduced; these are generated as a number of equiprobable realisations. In the present paper, we apply these techniques to acoustic data from an acoustic survey of North Sea herring. Sequential gaussian simulations are used to generate realisations for fish length and values of the nautical area scattering coefficient. These are then combined to produce realisations of herring density. The combined set of multiple realisations is then used to provide confidence intervals for the global abundance estimate: 95% of the herring abundance estimates are between 5677 and 6271 millions of individuals. Although the method presented in this paper contributes to the assessment of total uncertainty for acoustic surveys, the approach may have suffered from bias due to the use of off-the-shelf data transformation algorithms on fisheries acoustic data, which are often very positively skewed. We discuss this limitation and propose corrections for future work.