Can anybody please let me know about any good effective remedy for getting rid of undereye dark circles ?

"allergic shiners": The most common cause for the dark circles under the eyes is know as "allergic shiners." as the name implies, this is caused by environmental allergies. Avoidance to things you are allergic to is the best way to et rid of allergic shiners. Additionally, antihistamines, such as claritin, (loratadine) allegra, or zyrtec may also be helpful. See your doctor or allergist for a more definitive treatment plan.

Under eye circles: Unfortunately no. Avoid spending money on costly creams because they typically don't work. Sometimes dark circles can be a symptom of something else such as addisons disease but often it is due to thin skin and the hue of the underlying blood vessels and muscle. Cosmetics that cover up can help the appearance.