The　classical　firefighter　problem,　introduced　by　Bert　Hartnell　in　1995,　is　a　deterministic　discrete-time　model　of　the　spread　and　defence　of　fire,　rumor,　or　disease.　In　contrast　to　the　generally　＂discontinuous＂　firefighter　movements　of　the　classical　setting,　we　propose　in　the　paper　the　continuous　firefighting　model.　Given　an　undirected　graph　G,　at　time　0,　all　vertices　of　G　are　undefended,　and　fires　break　out　on　one　or　multiple　different　vertices　of　G.　At　each　subsequent　time　step,　the　fire　spreads　from　each　burning　vertex　to　all　of　its　undefended　neighbors.　A　finite　number　of　firefighters　are　available　to　be　assigned　on　some　vertices　of　G　at　time　1,　and　each　firefighter　can　only　move　from　his　current　location　(vertex)　to　one　of　his　neighbors　or　stay　still　at　each　time　step.　A　vertex　is　defended　if　some　firefighter　reaches　it　no　later　than　the　fire.　We　study　fire　containment　on　infinite　k-dimensional　square　grids　under　the　continuous　firefighting　model.　We　show　that　the　minimum　number　of　firefighters　needed　is　exactly　2k　for　single　fire,　and　5　for　multiple　fires　when　k　=　2.