Two-dimensional cell culturing has proven inadequate as a reliable preclinical tumour model due to many inherent limitations. Hence, novel three-dimensional (3D) cell culture models are needed, which in many aspects can mimic a native tumour with 3D extracellular matrix. Here, we present a 3D electrospun polycaprolactone (PCL) mesh mimicking the collagen network of tissue. The naturally hydrophobic PCL mesh was subjected to O2 plasma treatment to obtain hydrophilic fibres. Biocompatibility tests performed using L929 fibroblasts show that the 3D PCL fibre unit compartments were non-toxic. The human breast cancer cell lines MCF-7 and JIMT-1, the normal-like human breast cell line MCF-10A, and human adult fibroblast were cultured in PCL meshes and cell proliferation was monitored using the AlamarBlue® assay. Confocal microscopy and cryosectioning show that the cells penetrated deep into the fibre mesh within 1 week of cell culturing. The cancer cells form spheroids with the cells attaching mainly to each other and partly to the fibres. The human adult fibroblasts stretch out along the fibres while the MCF-10A cells stretch between fibres. Overall, we show that normal and cancer cells thrive in the 3D meshes cultured in fetal bovine free medium which eliminates the use of collagen as an extracellular matrix support.