Carcinogenesis, the process by which cells of the organism undergo transfor- mations, which eventually lead to formation of malignant tumours, is a process, the nature of which is sub ject of vigorous current research and much contro- versy. Two main theories of early cancer are (i) the clonal theory, by which a tumour can be traced to a single “first” malignant cell and (ii) the cancerisation field theory, by which a population of similar cells is responding similarly to a carcinogen. The field theory better explains multiple primary tumours and existence of spatially distributed pre-malignant areas in a tissue. We designed a series of mathematical models, in which spatial diffusion of growth factors, cell growth, mutations and mutualism among early cancer cells are taken into account. The models have the form of reaction-diffusion equations coupled with ordinary differential equations. They describe how early growth occurs over lin- ear structures in the tissue, such as alveoli in the lungs or ducts in the breast. We use analytic and computational methods to demonstrate that models generate spatial patterns, analogous to those in the transition from atypical adenoma- tous hyperplasia (AAH) to bronchoalveolar carcinoma (BAC) of the lung. One important biological conclusion from modelling is that diffusion of growth fac- tors dramatically alters the growth dynamics, leading to effects such as rapid exponential growth following a period of apparent stability and formation of spatial patterns (spikes and plateaus). Biologically, our results are consistent with a version of cancerisation field theory.