An accurate prediction of floor accelerations is crucial for estimating damage to contents and non-structural components in a building. Oversimplifying the nature of acceleration demands might result in biased estimates of building damage and consequently bias in the calculation of economic losses. However, given the relative novelty of multi-storey tall timber buildings, dedicated studies and models of their seismic acceleration demands are lacking. The need for these is stressed further when we recognise that the behaviour of walled timber structures is decidedly different from that of other conventional structural types. In this study, we apply modern data-driven approaches to evaluate efficient intensity measures (IMs) and develop regression models for predicting the peak floor acceleration (PFA) of multi-storey cross-laminated timber (CLT) buildings. Twenty-four IMs are evaluated and their prediction performance is compared. The sensitivity of acceleration demands to different IMs over a wide range of CLT buildings is investigated. We perform a systematic feature selection process using three different data-driven techniques. The selected features are then used to develop nine regression models to estimate PFA. Various modelling techniques, consisting of conventional (Linear and Polynomial regressions) as well as machine learning algorithms (Decision trees, Random forest, K-nearest neighbour, and Support vector regression) are used. The dataset used to train the models is obtained from numerical results of 69 CLT building models with variations in building height, panel fragmentation levels, and q-factors (ductility levels) subjected to a large set of strong earthquakes. After assessing the accuracy of our model predictions, their PFA estimates obtained are compared against previous research and design codes. Finally, simplified expressions for estimating peak floor accelerations in CLT structures are provided for practical purposes.