In my opinion, you could use:

1) a 2D model on the plane Oxz for y = 0 where z is the through the thickness direction and, then, use plane strain key-option for the element (es. PLANE183 with KEYOPT(3)=2).

2) a 3D model of unit width along y and impose all the displacements along y equal to zero (besides the simply supported boundary conditions). In this case, you can apply directly a line load (I use the trick of a dummy beam to transfer the load to 3D elements, but there should be a special, and more efficient, element or way for that). To save dofs, you could exploit the symmetry at x=0.

I believe a 1D solution is more suitable for a plain stress problem, but I could be wrong (I did not check the documentation thoroughly).

I hope it might help.

Just for me to learn, could you, please, post a short description of your final (working) solution (that is not necessary the same I just suggested)?

1D elements use Timoshenko's theory, therefore, there is both plane strain (from the kinematics) and plane stress (to constrast Poisson's locking). The results, then, in principle should not be very different from 2D and 3D solutions I proposed in the previous post (provided the plate is not too much thick). For beam elements, you should define a cross-section the width of which is used for obtaining the resultant force (from the actual line load) to be applied to your 1D model.

KEYOPT(3)=2 gives plain  strain in z-direction . but in my case plain strain is in y -direction . and also I can apply force along x and y direction only (while my force is in z-dir). 

even if I model my plate in x-z direction and give KEYOPT(3)=2 it will not mesh it as z DOF is completely removed. 

You should make your rectangle [-d,+d]x[-h/2,+h/2]  (h is the plate thickness) in the plane Oxz (remember to change the working plane orientation) and not on the Oxy one.

The idea is to get rid of the y dimensions (the infinite one) by cutting a slice at y=0.

Thanks Dr. Gaetano Giunta

Macro for this problem(modified):

finish

/clear

/PREP7

MP,EX,1,120e9 ! Young's modulus

MP,PRXY,1,0.33 ! Poisson's ratio

MP,DENS,1,7000 ! Density

ET,1,PLANE183 ! PLANE 183 ELEMENT

KEYOPT,1,3,2 ! PLANE STRAIN

k,1,0.5,-0.005,0 ! Defining Key points for plate cross section

k,2,0.5,0.005,0

k,3,-0.5,0.005,0

k,4,-0.5,-0.005,0

FLST,2,4,3 ! Creating cross section Area

FITEM,2,1

FITEM,2,2

FITEM,2,3

FITEM,2,4

A,P51X

esize,0.01 !Meshing

amesh,all

NSEL,S,LOC,X,-0.5 !Applying BC at edge: simply supported

NSEL,R,LOC,Y,0

D,all, ,,, , ,UX,UY

allsel

NSEL,S,LOC,X,0.5

NSEL,R,LOC,Y,0

D,all, ,,, , ,UX,UY

allsel

NSEL,S,LOC,X,0

NSEL,R,LOC,Y,0

F,ALL,FY,-1 !Applying Force

allsel

FINISH

/SOLU

With above formulation results are matching with analytic solution.

I want to solve same problem using beam element so what changes i have to do?

In your previous post  " 1D elements use Timoshenko's theory "  : I did not understand how to reduce UDL to point load on beam ?as well as what section dimension should i assign?

You should use a beam element with rectangular cross-section where the thickness is the thickness of your plate and a unit deepth (d) (although this should be irrelevant). I suggest a unit deepth so that the UDL (q) and its resulting force (F=qd) are equal in value. The value of d can be freely chosen (but the resulting force should be coherently computed) since, according to the analytical solution, the transverse displacement (v) is propostional to  F/I and d in the force (F=qd) and in the moment of inertia (I proportional to d) cancel out each other.