A strong edge colouring of a graph $G$ is a proper edge colouring such that every path of length 3 uses three colours. In this paper, we give some upper bounds for the minimum number of colours in a strong edge colouring of subcubic graphs as a function of the maximum average degree. We also prove the NP-completeness of the strong edge $k$-colouring problem for some restricted classes of subcubic planar graphs when $k=4,5,6$.