If particles are of finite size they are not fundamental and must be made of something else. Fundamental particles are pointlike and have no measurable size. But pointlike objects lead to infinities.
The electric field on the surface 
which goes to infinity as the radius goes to zero.
String theory is based on the idea that fundamental particles are not pointlike but stringlike. Particles can be closed or open strings.
The theory is formulated in a space of 10 or more dimensions. This idea is based on the work by Kaluza and Klein in the 1920s.
They added a fifth dimension to the regular three space plus one time dimensions. This fifth dimension is `curled up' and has no effect on usual physics.
Normally one sees a line with 3 space
dimensions plus time. At a magnification of 
one sees a `pipe' with 4 space dimensions plus time. One can define field
in this 5 dimensional space which in 4 dimensions looks like the field
equations of general relativity plus Maxwell's equations. This gave a
connection between electromagnetism and general relativity. There were
some problems and it was not pursued at th etime. The interest has now
been revived and extended to more dimensions.
In superstring theory the scattering of two particles might look like this (but in more dimensions)
The theory is still being developed and is a long way from `a theory of everything' but has many encouraging features.
Information provided by: http://hepwww.ph.qmw.ac.uk