Experimental results for the cracking of heterogeneous clay samples during desiccation are reported, and an associated numerical model is developed for comparison. The clay samples contain embedded rigid inclusions to induce heterogeneous strain fields during drying. The crack paths and local strain fields are monitored during the desiccation process using digital image correlation. A numerical phase field model for crack initiation and propagation is introduced and compared with the experimental results. A qualitative agreement is found for the obtained crack paths, whereas discrepancies remain for the local strain fields. A discussion regarding the comparison between the experimental results and model is provided.