Why Black should play Max Lange attack, when its favorable for white only.? In Max Lange attack..when white is giving gambit of d and e pawns and can grab a piece or good attacking favorable position. Then why black should accept it? Is there any solid defense against it?
I hope you are talking about the below line . " 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.d4 exd4 5.0-0 Bc5 6.e5 " 

The Best response to the above line from Black is 6) ..d5! .

7.exf6 dxc4 8.Re1+ Be6 9.Ng5 Qd5 (9...Qxf6?? 10.Nxe6 fxe6 11.Qh5+ followed by 12.Qxc5 is a notorious trap) 10.Nc3 Qf5 (10...dxc3?? 11.Qxd5 wins, since 11...Bxd5 is illegal) 11.Nce4 0-0-0 with complicated play.

True the Theory of max lange extends long but it is refutable from Black side . Black needs to be extra cautious to avert White's Activity . Black should try castling Q-side . One line goes as follows 

"1. e4 e5   2. Nf3 Nc6   3. Bc4 Bc5   4. d4 exd4   5. O-O Nf6   6. e5 d5   7. exf6 dxc4   8. Re1+ Be6   9. Ng5 Qd5   10. Nc3 Qf5   11. Nce4 O-O-O   "

If on move no 9)White captures the g7 pawn then advantage goes to Black's side .

" 1. e4 e5   2. Nf3 Nc6   3. Bc4 Bc5   4. d4 exd4   5. O-O Nf6   6. e5 d5   7. exf6 dxc4   8. Re1+ Be6   9. fxg7 Rg8  " 

The White Player is the Man with the Plan and he needs to remember each move precisely else one incorrect move and the Tables will turn towards Black side .

The most aggressive line is " 1. e4 e5   2. Nf3 Nc6   3. Bc4 Bc5   4. d4 exd4   5. O-O Nf6   6. e5 d5   7. exf6 dxc4   8. Re1+ Be6   9. Ng5 Qd5   10. Nc3 Qf5   11. Nce4 O-O-O   12. Nxe6 fxe6   13. g4 Qe5   " . Here the Game depends on who is a better player .

If you are still unsure &amp; afraid to play Max Lange then I would suggest that you try Philidor Defense as Black which is safe and does not involve too many gambits line . 

In top level Tournaments you can rarely see Max Lange nowdays .