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In v a r i o u s s i t u a t i o n s o f f i n i t e element a n a l y s i s o f c r a c k p r o p a g at i o n p r o b l e m s i t would be d e s i r a b l e to have an element a l l o w i n g f o r an a r b i t r a r y p o s i t i o n o f t h e c r a c k t i p , Fig. l a . For t h e sake o f computat i o n a l e f f i c i e n c y , t h e element s h o u l d a l s o a c c o u n t f o r t h e s i n g u l a r i t i e s around t h e c r a c k t i p . Since s p e c i a l c r a c k t i p e l e m e n t s o f f e r c o n s i d e ra b l e d i s a d v a n t a g e s such as l a c k o f c o n s t a n t s t r a i n modes, l a c k o f comp a t i b i l i t y with n e i g h b o r i n g e l e m e n t s , and need some e f f o r t to implement in e x i s t i n g p r o g r a m s , i t f e l t n a t u r a l to t r y to use the 8-noded i s o p a r am e t r i c e l e m e n t . P r e v i o u s i n v e s t i g a t o r s have documented t h e e f f i c i e n c y o f t h i s element in c o m p u t a t i o n o f s t r e s s i n t e n s i t y f a c t o r s [ 1 -5 ] . By combining f o u r such e l e m e n t s a c c o r d i n g t o Fig. lb and a l l o w i n g f o r an a r b i t r a r y p o s i t i o n o f node N, t h e d e s i r e d element i s o b t a i n e d . The s i n g u l a r i t y i s a c h i e v e d in t h e u s u a l manner [1-5] by p l a c i n g s i d e nodes on s i d e s c o n n e c t e d with t h e crack t i p a t t h e q u a r t e r p o i n t s . The a l l o w a n c e f o r an a r b i t r a r y p o s i t i o n o f node N may l e a d to d e g e n e r at i o n o f e l e m e n t s A o r B i n t o t r i a n g l e s . This p o s e s , however, no p r o blems [5]. The c o m p u t a t i o n a l e f f i c i e n c y o f t h e p r o p o s e d t e c h n i q u e i s i l l u st r a t e d f o r t h e c a s e o f a c e n t r a l l y c r a c k e d s t r i p s u b j e c t e d to u n i f o r m t e n s i o n , Fig. 2. An a p p r o x i m a t e f o r m u l a f o r K I which i s a c c u r a t e to 1% has been given f o r t h i s case in r e f e r e n c e s [6] and [7]. K I = o / ( = a ) [ 1 -0 . 5 ( a / b ) + O.326(a/b)2]//(1-a/b) (1) o One q u a r t e r o f t h e p l a t e in Fig. 2 was s u b d i v i d e d i n t o 40 e l e m e n t s acc o r d i n g t o Fig. 3, c o m p r i s i n g in t o t a l 145 nodes.The s e m i -c r a c k l e n g t h a was v a r i e d between 0.6b and 0.5b (b=10) by g i v i n g node 15 (and nodes on a d j o i n i n g s i d e s ) a p p r o p r i a t e c o o r d i n a t e s , Fig. 4. K I was c a lc u l a t e d from t h e J -i n t e g r a l e v a l u a t e d along an i n t e g r a t i o n p a t h t h r o u g h Gauss p o i n t s ; see Fig. 3. The program PIFEM [8] was used f o r the num-