Eucalyptus trees are fairly hardy, but not even these survivors should be asked to compete with grass. When grass grows over the roots of a tree, it robs the tree of vital nutrients. And because grass is watered frequently and shallowly, it will cause your eucalyptus roots to grow shallow instead of deep in their search for water. Once you take your eucalyptus tree's health into consideration, you can grow your grass as you would in any other lawn environment.
Uproot any grass growing inside and within 3 feet of your eucalyptus tree's drip line. Take care not to disturb the roots of the tree, but be sure to take the grass roots along with the blades.
Spread a layer of mulch 2 to 3 inches deep around your eucalyptus tree. Keep the mulch 1 foot away from the base of the tree and extend it approximately 2 feet beyond its drip line. The mulch will keep grass and weeds from competing with the tree for nutrients.
Plant shade-resistant varieties of grass in areas that are frequently covered by your eucalyptus tree's shadow. This grass will grow more vigorously and resist weed growth.
Mow your grass regularly. The height at which you keep your grass will be dictated by the variety that you have planted. Some varieties should be kept as low as 1/4 inch and others can be kept as long as 4 inches, but whatever your grass's requirements, do not mow more than 1/3 of its height at any one time.
Fertilize the grass with at least two equal applications of fertilizer, typically given in the spring and again in the fall. Certain varieties of grass need smaller, more frequent fertilizer applications than others.
Water your lawn with 1 to 2 inches of water whenever the top few inches of the soil dries out or the grass blades wilt.
Remove thatch with a vertical mower when it builds up to 2 inches in height. The best time to de-thatch your lawn is at the beginning of its growing season.