This paper proposes a new mathematical model for locating k-obnoxious facilities Here a vertex covering k-obnoxious facilities location problem on a plane has been modelled by combining it as a combination of three interacting criteria as follows: 1) maximise the minimum distances between any existing point and any variable point as well as between any pair of variable points; 2) maximise the number of existing points covered by various respective variable points; 3) minimise the overall importance of the various existing points associated to the various variable facility points. A nonlinear programming iterative algorithm for locating k-obnoxious facilities has been developed. The algorithm developed here is a generalised iterative algorithm. It has been proved that the optimal solution obtained by the algorithm is the non-dominated solution of the original multi-objective problem. Rectilinear distance norm has been considered as the distance measure as it is more appropriate to the various realistic situations.